Recent questions tagged inflection

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Points of inflection for $f(x)=3x^5 - 10x^3 + 7$

asked Mar 1 in Mathematics by anonymous | 191 views

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What is the integral of a function?

asked Jan 27 in Mathematics by ♦AstraNova Diamond (55.3k points) | 140 views

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Rewrite $\cos 3 \mathrm{~A}$ in terms of $\cos \mathrm{A}$

asked Jan 24 in Mathematics by ♦AstraNova Diamond (55.3k points) | 153 views

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Rewrite $\sin 3 \alpha$ in terms of $\sin \alpha$ :

asked Jan 24 in Mathematics by ♦AstraNova Diamond (55.3k points) | 142 views

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Find the integral of the function $f(x) = \frac{3}{x^2}$.

asked Jan 10 in Mathematics by ♦Acalytica Platinum (97.7k points) | 111 views

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If $\lim _{x \rightarrow 1} \frac{x+x^2+x^3+\ldots . .+x^n-n}{x-1}=820,(n \in N)$ then the value of $\mathrm{n}$ is equal to

asked Nov 29, 2022 in Mathematics by ♦Maths Genie Bronze Status (8.8k points) | 140 views

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Evaluate $\int \frac{x+1}{x^2+4 x+8} d x$.

asked Nov 22, 2022 in Mathematics by ♦Acalytica Platinum (97.7k points) | 123 views

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Evaluate $\int \frac{x^3}{(x-2)(x+3)} d x$.

asked Nov 22, 2022 in Mathematics by ♦Acalytica Platinum (97.7k points) | 132 views

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Rewrite $\int \frac{x^3}{(x-2)(x+3)} d x$ in terms of an integral with a numerator that has degree less than 2.

asked Nov 22, 2022 in Mathematics by ♦Acalytica Platinum (97.7k points) | 142 views

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Find $\int \frac{x^3}{(3-2 x)^5} d x$.

asked Nov 22, 2022 in Mathematics by ♦Acalytica Platinum (97.7k points) | 127 views

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Evaluate $\int \sec ^3 x d x$

asked Nov 22, 2022 in Mathematics by ♦Acalytica Platinum (97.7k points) | 156 views

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Evaluate the integral $\int x \ln x d x$

asked Nov 22, 2022 in Mathematics by ♦Acalytica Platinum (97.7k points) | 137 views

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Evaluate $\int \sqrt{4-9 x^2} d x$

asked Nov 22, 2022 in Mathematics by ♦Acalytica Platinum (97.7k points) | 121 views

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Evaluate $\int \sqrt{1-x^2} d x$.

asked Nov 22, 2022 in Mathematics by ♦Acalytica Platinum (97.7k points) | 157 views

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What is a vertical asymptote?

asked Sep 12, 2022 in Mathematics by ♦AstraNova Diamond (55.3k points) | 142 views

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Evaluate the following limits.

asked Sep 12, 2022 in Mathematics by ♦AstraNova Diamond (55.3k points) | 173 views

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Let $\lim _{x \rightarrow 2} f(x)=2, \quad \lim _{x \rightarrow 2} g(x)=3 \quad$ and $\quad p(x)=3 x^2-5 x+7 .$ Find the following limits:

asked Sep 12, 2022 in Mathematics by ♦AstraNova Diamond (55.3k points) | 165 views

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Describe three situations where $\lim _{x \rightarrow c} f(x)$ does not exist.

asked Sep 12, 2022 in Mathematics by ♦AstraNova Diamond (55.3k points) | 161 views

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Integral part of $(\sqrt{2}+1)^{6}$ is

asked Aug 15, 2022 in Mathematics by ♦AstraNova Diamond (55.3k points) | 162 views

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Suppose $f^{\prime}$ is continuous on $[a, b]$ and $\varepsilon>0$. Prove that there exists $\delta>0$ such that \[ \left|\frac{f(t)-f(x)}{t-x}-f^{\prime}(x)\right|<\varepsilon \]

asked Jul 5, 2022 in Mathematics by ♦AstraNova Diamond (55.3k points) | 195 views

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Suppose $f^{\prime}(x)$ and $g^{\prime}(x)$ exist, $g^{\prime}(x) \neq 0$, and $f(x)=g(x)=0$. Prove that \[ \lim _{t \rightarrow x} \frac{f(t)}{g(t)}=\frac{f^{\prime}(x)}{g^{\prime}(x)} . \]

asked Jul 5, 2022 in Mathematics by ♦AstraNova Diamond (55.3k points) | 121 views

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Suppose $f$ is a real, continuously differentiable function on $[a, b]$, $f(a)=f(b)=0$, and \[ \int_{a}^{b} f^{2}(x) d x=1 \] Prove that

asked Jul 5, 2022 in Mathematics by ♦AstraNova Diamond (55.3k points) | 241 views

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If $f(x)=0$ for all irrational $x, f(x)=1$ for all rational $x$, prove that $f \notin \mathcal{R}$ on $[a, b]$ for any $a<b$.

asked Jul 5, 2022 in Mathematics by ♦AstraNova Diamond (55.3k points) | 206 views

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Suppose $f \geq 0, f$ is continuous on $[a, b]$, and $\int_{a}^{b} f(x) d x=0$. Prove that $f(x)=0$ for all $x \in[a, b]$.

asked Jul 5, 2022 in Mathematics by ♦AstraNova Diamond (55.3k points) | 171 views

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Suppose $\alpha$ increases on $[a, b], a \leq x_{0} \leq b, \alpha$ is continuous at $x_{0}$, $f\left(x_{0}\right)=1$, and $f(x)=0$ if $x \neq x_{0}$. Prove that $\bar{f} \in \mathcal{R}(\alpha)$ and that $\int f d \alpha=0$.

asked Jul 5, 2022 in Mathematics by ♦AstraNova Diamond (55.3k points) | 249 views

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Prove a pointwise version of Fejér's Theorem: If $f \in \mathcal{R}$ and $f(x+), f(x-)$ exist for some $x$, then \[ \lim _{N \rightarrow \infty} \sigma_{N}(f ; x)=\frac{1}{2}[f(x+)+f(x-)] . \]

asked Jul 5, 2022 in Mathematics by ♦AstraNova Diamond (55.3k points) | 144 views

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Suppose $f \in \mathcal{R}$ on $[0, A]$ for all $A<\infty$, and $f(x) \rightarrow 1$ as $x \rightarrow+\infty$. Prove that \[ \lim _{t \rightarrow 0} \int_{0}^{\infty} e^{-t x} f(x) d x=1 \quad(t>0) \]

asked Jul 5, 2022 in Mathematics by ♦AstraNova Diamond (55.3k points) | 201 views

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For $i=1,2,3, \ldots$, let $\varphi_{i} \in \mathcal{C}\left(R^{1}\right)$ have support in $\left(2^{-i}, 2^{1-i}\right)$, such that $\int \varphi_{i}=1$. Put

asked Jul 5, 2022 in Mathematics by ♦AstraNova Diamond (55.3k points) | 173 views

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Suppose $f \in \mathcal{L}^{2}(\mu), g \in L^{2}(\mu)$. Prove that \[ \left|\int f \bar{g} d \mu\right|^{2}=\int|f|^{2} d \mu \int|g|^{2} d \mu \] if and only if there is a constant $c$ such that $g(x)=c f(x)$ almost everywhere.

asked Jul 5, 2022 in Mathematics by ♦AstraNova Diamond (55.3k points) | 163 views

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If $f \in \mathcal{R}$ on $[a, b]$ and if $F(x)=\int_{a}^{x} f(t) d t$, prove that $F^{\prime}(x)=$ $f(x)$ almost everywhere on $[a, b]$.

asked Jul 5, 2022 in Mathematics by ♦AstraNova Diamond (55.3k points) | 169 views

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If $f \geq 0$ and $\int_{E} f d \mu=0$, prove that $f(x)=0$ almost everywhere on $E$.

asked Jul 5, 2022 in Mathematics by ♦Acalytica Platinum (97.7k points) | 169 views

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Evaluate $f(x)=\int_{0}^{x} \frac{1}{\sqrt{1+t^{2}}} d t$

asked Jul 2, 2022 in Mathematics by ♦AstraNova Diamond (55.3k points) | 163 views

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Solve the integral equation \[ \int_{0}^{x}\left((x-y)^{2}-2\right) f(y) d y=-4 x \] applying differentiation and the solving the resulting differential equation.

asked Jul 2, 2022 in Mathematics by ♦AstraNova Diamond (55.3k points) | 187 views

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Solve \[ \int_{0}^{x} e^{-x} f(s) d s=e^{-x}+x-1 \] applying differentiation.

asked Jul 1, 2022 in Mathematics by ♦AstraNova Diamond (55.3k points) | 145 views

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Evaluate the integral $f(x)=\int_{0}^{x} \frac{1}{\sqrt{1+t^{2}}} d t$

asked Jun 27, 2022 in Mathematics by ♦AstraNova Diamond (55.3k points) | 154 views

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Evaluate $x^2+49=0$

asked Jun 22, 2022 in Mathematics by ♦Acalytica Platinum (97.7k points) | 110 views

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Evaluate $\int \frac{1}{\sqrt[4]{x}+3} d x$

asked Jun 22, 2022 in Mathematics by ♦Acalytica Platinum (97.7k points) | 141 views

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Evaluate the integral $\int x \ln x d x$

asked Jun 21, 2022 in Mathematics by ♦Acalytica Platinum (97.7k points) | 149 views

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Calculate $\int 5 x^{4} d x$

asked May 31, 2022 in Mathematics by ♦AstraNova Diamond (55.3k points) | 170 views

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Calculate $\int \frac{1}{\sqrt[3]{x}} d x$

asked May 31, 2022 in Mathematics by ♦AstraNova Diamond (55.3k points) | 194 views

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State the definition of a inflection point of a function $f$.

asked Feb 4, 2022 in Mathematics by ♦AstraNova Diamond (55.3k points) | 244 views

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What is the general antiderivative of $6 x^{2}+2 x+5 ?$

asked Feb 4, 2022 in Mathematics by ♦AstraNova Diamond (55.3k points) | 174 views

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Sketch the graph of $f(x)=\frac{\ln x}{x}$, showing all extrema.

asked Feb 4, 2022 in Mathematics by ♦AstraNova Diamond (55.3k points) | 164 views

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Find the general form for the following antiderivative: $\int \frac{z}{z^{2}+9} d z$

asked Feb 4, 2022 in Mathematics by ♦AstraNova Diamond (55.3k points) | 191 views

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The function $f(x)=\dfrac{x^{3}-6 x}{x^{2}-4}$ has ...

asked Jan 13, 2022 in Mathematics by ♦Acalytica Platinum (97.7k points) | 160 views

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Evaluate the integral: $\int \dfrac{3 x+2}{\sqrt{4-3 x^{2}}} d x$

asked Jan 13, 2022 in Mathematics by ♦Acalytica Platinum (97.7k points) | 201 views

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Evaluate the integral: $\int_{0}^{\pi} 2 x \cos 2 x d x$

asked Jan 13, 2022 in Mathematics by ♦Acalytica Platinum (97.7k points) | 217 views

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Evaluate $\int \dfrac{\ln z}{(1+z)^{2}} d z$

asked Jan 13, 2022 in Mathematics by ♦Acalytica Platinum (97.7k points) | 251 views

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Evaluate the following integral: $\int \frac{t}{\sqrt{t^{4}-1}} d t$.

asked Jan 13, 2022 in Mathematics by ♦Acalytica Platinum (97.7k points) | 195 views

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Evaluate the integral $\int_{1}^{2} \dfrac{2 s-2}{\sqrt{-s^{2}+2 s+3}} d s$

asked Jan 13, 2022 in Mathematics by ♦Acalytica Platinum (97.7k points) | 284 views

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