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1 votes
2 answers
271
GATE Overflow | Mock GATE | Test 1 | Question: 19
Evaluate the limit: $ \lim_{x \to -3} \frac{\sqrt{2x+22}-4}{x+3}$ $\frac{1}{2}$ $\frac{1}{4}$ $\frac{1}{8}$ $\frac{1}{16}$
Evaluate the limit:$$ \lim_{x \to -3} \frac{\sqrt{2x+22}-4}{x+3}$$$\frac{1}{2}$$\frac{1}{4}$$\frac{1}{8}$$\frac{1}{16}$
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0 votes
0 answers
272
Shortcut Method to find Maxima and Minima in Calculus
https://www.youtube.com/watch?v=tyiQLindzCE This is a great video but covers formula for cubic root what about for any given equation x^n,what would be the solution?
https://www.youtube.com/watch?v=tyiQLindzCEThis is a great video but covers formula for cubic root what about for any given equation x^n,what would be the solution?
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0 votes
0 answers
273
self doubt
How to solve these questions $(1)$ $I=\int_{0}^{1}(xlogx)^{4}dx$ $(2)$ $I=\frac{1}{\sqrt{2\pi}}\int_{0}^{\infty}e^{\frac{-x^{2}}{8}}dx$ $(3)$ $I=\int_{0}^{\infty}x^{\frac{1}{4}}.e^{-\sqrt{x}}dx$
How to solve these questions$(1)$ $I=\int_{0}^{1}(xlogx)^{4}dx$$(2)$ $I=\frac{1}{\sqrt{2\pi}}\int_{0}^{\infty}e^{\frac{-x^{2}}{8}}dx$$(3)$ $I=\int_{0}^{\infty}x^{\frac{...
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7 votes
2 answers
274
TIFR CSE 2019 | Part A | Question: 13
Consider the integral $\int^{1}_{0} \frac{x^{300}}{1+x^2+x^3} dx$ What is the value of this integral correct up to two decimal places? $0.00$ $0.02$ $0.10$ $0.33$ $1.00$
Consider the integral$$\int^{1}_{0} \frac{x^{300}}{1+x^2+x^3} dx$$What is the value of this integral correct up to two decimal places?$0.00$$0.02$$0.10$$0.33$$1.00$
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2 votes
1 answer
277
NIELIT 2018-15
The value of $\int_1^2 \int_0^{x^2} x \: dy \: dx$ is: $\frac{15}{4}$ $\frac{5}{4}$ $\frac{3}{4}$ $\frac{2}{3}$
The value of $\int_1^2 \int_0^{x^2} x \: dy \: dx$ is:$\frac{15}{4}$$\frac{5}{4}$$\frac{3}{4}$$\frac{2}{3}$
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0 votes
1 answer
278
GradeUp quiz-Maxima minima
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0 votes
0 answers
279
Gilbert Strang
$\int_{1}^{∞}\frac{dx}{x^6+1}$
$\int_{1}^{∞}\frac{dx}{x^6+1}$
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2 votes
1 answer
280
Calculus-Integration
$\int x^7.e^{x^4}dx$ How to do this?
$\int x^7.e^{x^4}dx$How to do this?
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0 votes
1 answer
281
Integration
$\int_{0}^{1}\frac{x^{\alpha }-1}{logx}dx$ where $\alpha>0$
$\int_{0}^{1}\frac{x^{\alpha }-1}{logx}dx$ where $\alpha>0$
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0 votes
1 answer
282
Gilbert Strang
$\int_{}^{}\frac{x dx}{\sqrt{x^4-1}}$
$\int_{}^{}\frac{x dx}{\sqrt{x^4-1}}$
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2 votes
1 answer
283
Got from friend
Find the limit of the given expression $\lim_{x\to\frac{\pi}{2}}\left ( \sec x-\frac{1}{1-\sin x} \right )$
Find the limit of the given expression$\lim_{x\to\frac{\pi}{2}}\left ( \sec x-\frac{1}{1-\sin x} \right )$
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0 votes
1 answer
284
Gilbert Strang
Differentiate y=$x^{-1/lnx}$
Differentiatey=$x^{-1/lnx}$
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0 votes
0 answers
285
Gilbert Strang
$\int_{0}^{1}(x^2+1)^4dx$
$\int_{0}^{1}(x^2+1)^4dx$
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0 votes
1 answer
286
Gilbert Strang
$\int \frac{x^3}{\sqrt{1+x^2}}.dx$
$\int \frac{x^3}{\sqrt{1+x^2}}.dx$
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0 votes
1 answer
288
limits
Find the limit $\operatorname { lit } _ { x \rightarrow 1 } \left\{ \left( \frac { 1 + x } { 2 + x } \right) ^ { \left( \frac { 1 - \sqrt { x } } { 1 - x } \right) } \right\}$
Find the limit$\operatorname { lit } _ { x \rightarrow 1 } \left\{ \left( \frac { 1 + x } { 2 + x } \right) ^ { \left( \frac { 1 - \sqrt { x } } { 1 - x } \right) } \righ...
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1 votes
1 answer
289
Calculus-Definite Integral
What is the value of $\int_0^\pi log(1+cosx)dx$
What is the value of $\int_0^\pi log(1+cosx)dx$
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0 votes
1 answer
290
Gilbert Strang Doubt
Locate the inflection points and region where f(x) is concave up or down f(x)=$-x^3+x^2+x$
Locate the inflection points and region where f(x) is concave up or downf(x)=$-x^3+x^2+x$
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0 votes
1 answer
291
Maxima and Minima
Find the stationary points, maxima and minima f(x)=|x+1|+|x-1| , -3<=x<=2
Find the stationary points, maxima and minimaf(x)=|x+1|+|x-1| , -3<=x<=2
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0 votes
1 answer
292
Integration
Solve $\int_{0}^{\pi }sin^{5}\frac{x}{2}dx$
Solve$\int_{0}^{\pi }sin^{5}\frac{x}{2}dx$
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0 votes
1 answer
294
Differentiability
$\varphi \left ( x \right )=x^{2}\cos \frac{1}{x}$ when $x\neq 0$ $=0$ when $x=0$ Is it differentiable at $x=0$? Is it continuous ?
$\varphi \left ( x \right )=x^{2}\cos \frac{1}{x}$ when $x\neq 0$ $=0$ when $x=0$Is it differentiable at $x=0$?Is it continuous ?
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0 votes
2 answers
295
ISI2016-PCB-A-2
Let $n$ be a fixed positive integer. For any real number $x,$ if for some integer $q,$ $x=qn+r, \: \: \: 0 \leq r < n,$ then we define $x \text{ mod } n=r$. Specify the points of discontinuity of the function $f(x)=x \text{ mod } 3$ with proper reasoning.
Let $n$ be a fixed positive integer. For any real number $x,$ if for some integer $q,$ $$x=qn+r, \: \: \: 0 \leq r < n,$$ then we define $x \text{ mod } n=r$.Specify the...
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0 votes
0 answers
296
calculus
what is difference between this and in questions if asked to find derivative or check differentiable or not, which formula should i use? 1) $lim_{h\rightarrow 0} \frac{f(a+h)-f(a)}{h}$ 2) $lim_{x\rightarrow a} \frac{f(x)-f(a)}{x-a}$
what is difference between this and in questions if asked to find derivative or check differentiable or not, which formula should i use?1) $lim_{h\rightarrow 0} \frac{f(a...
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0 votes
2 answers
297
ISI2017-MMA-4
Let $S\subseteq \mathbb{R}$. Consider the statement “There exists a continuous function $f:S\rightarrow S$ such that $f(x) \neq x$ for all $x \in S.$ ” This statement is false if $S$ equals $[2,3]$ $(2,3]$ $[-3,-2] \cup [2,3]$ $(-\infty,\infty)$
Let $S\subseteq \mathbb{R}$. Consider the statement “There exists a continuous function $f:S\rightarrow S$ such that $f(x) \neq x$ for all $x \in S.$ ”This statement ...
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0 votes
1 answer
298
ISI2017-MMA-9
A function $y(x)$ that satisfies $\dfrac{dy}{dx}+4xy=x$ with the boundary condition $y(0)=0$ is $y(x)=(1-e^x)$ $y(x)=\frac{1}{4}(1-e^{-2x^2})$ $y(x)=\frac{1}{4}(1-e^{2x^2})$ $y(x)=\frac{1}{4}(1-\cos x)$
A function $y(x)$ that satisfies $\dfrac{dy}{dx}+4xy=x$ with the boundary condition $y(0)=0$ is$y(x)=(1-e^x)$$y(x)=\frac{1}{4}(1-e^{-2x^2})$$y(x)=\frac{1}{4}(1-e^{2x^2})$...
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0 votes
0 answers
300
ISI2017-MMA-14
Let $(v_n)$ be a sequence defined by $v_1=1$ and $v_{n+1}=\sqrt{v_n^2 +(\frac{1}{5})^n}$ for $n\geq1$. Then $\lim _{n\rightarrow \infty} v_n$ is $\sqrt{5/3}$ $\sqrt{5/4}$ $1$ nonexistent
Let $(v_n)$ be a sequence defined by $v_1=1$ and $v_{n+1}=\sqrt{v_n^2 +(\frac{1}{5})^n}$ for $n\geq1$. Then $\lim _{n\rightarrow \infty} v_n$ is$\sqrt{5/3}$$\sqrt{5/4}$$1...
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