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121
Mathematics for Natural Science
Simplify $(A\cup B)\cap (A\cup B')\cap (A - B)$ for a given non empty sets $A$ and $B$, where $(A\cap B) = \varnothing .$
Simplify $(A\cup B)\cap (A\cup B')\cap (A - B)$ for a given non empty sets $A$ and $B$, where $(A\cap B) = \varnothing .$
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1 votes
2 answers
122
Applied Mathematics Calculus and Limit Question
Evaluate the question of the following limits. $\lim_{x\rightarrow 1} \frac{x}{(x-1)^{2}}$
Evaluate the question of the following limits. $\lim_{x\rightarrow 1} \frac{x}{(x-1)^{2}}$
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1 answer
123
Applied Mathematics Derivative
Please find derivation of the following equation. Let $f(x)=e^{x^{2}}\ln x,$ then find, ${f}'(x)$.
Please find derivation of the following equation.Let $f(x)=e^{x^{2}}\ln x,$ then find, ${f}'(x)$.
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2 answers
124
Applied Mathematics Calculus and Limit Question
Evaluate the question of the following limits. $\lim_{x\rightarrow \infty} \frac{2x^{3}+3x-5}{5x^{3}+1}$
Evaluate the question of the following limits. $\lim_{x\rightarrow \infty} \frac{2x^{3}+3x-5}{5x^{3}+1}$
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0 votes
3 answers
125
Applied Mathematics Question
Let $f(x) = e^{x^2},$ then find $f''(x).$
Let $f(x) = e^{x^2},$ then find $f''(x).$
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126
iit kanpur Calculas practice question
Does there exist a differentiable function f : [0, 2] → R satisfying f(0) = −1, f(2) = 4 and f’(x) ≤ 2 for all x ∈ [0, 2]?
Does there exist a differentiable function f : [0, 2] → R satisfying f(0) = −1, f(2) = 4 and f’(x) ≤ 2 for all x ∈ [0, 2]?
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1 votes
2 answers
127
No of solution of the given equation
The Number of Points $x \in \Re$ for which $\sin ^{2} x-3x=5$ is , 0 1 more than one but finite $\infty$
The Number of Points $x \in \Re$ for which $\sin ^{2} x-3x=5$ is ,01more than one but finite$\infty$
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11 votes
4 answers
129
GATE CSE 2022 | Question: 24
The value of the following limit is ________________. $\lim_{x \rightarrow 0^{+}} \frac{\sqrt{x}}{1-e^{2\sqrt{x}}}$
The value of the following limit is ________________.$$\lim_{x \rightarrow 0^{+}} \frac{\sqrt{x}}{1-e^{2\sqrt{x}}}$$
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3 votes
1 answer
131
GATE Overflow Test Series | Mock GATE | Test 6 | Question: 31
The value of $\displaystyle{} \int_{0}^{\frac{\pi}{2}} \sin ^{4}x \cos^{4}x dx$ is _____ $\left(\dfrac{3\pi}{256}\right)$ $\left(\dfrac{5\pi}{768}\right)$ $\left(\dfrac{7\pi}{768}\right)$ $\left(\dfrac{3\pi}{384}\right)$
The value of $\displaystyle{} \int_{0}^{\frac{\pi}{2}} \sin ^{4}x \cos^{4}x dx$ is _____$\left(\dfrac{3\pi}{256}\right)$$\left(\dfrac{5\pi}{768}\right)$$\left(\dfrac{7\pi...
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2 answers
132
Calculus self doubt
Calculus looks difficult for me. Any resources to learn calculus for GATE
Calculus looks difficult for me. Any resources to learn calculus for GATE
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0 answers
133
Applied Test Series
What is the correct procedure to solve this limit ?
What is the correct procedure to solve this limit ?
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4 votes
1 answer
134
GATE CSE 1995 | Question: 7(B)
Compute without using power series expansion $\displaystyle \lim_{x \to 0} \frac{\sin x}{x}.$
Compute without using power series expansion $\displaystyle \lim_{x \to 0} \frac{\sin x}{x}.$
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4 votes
2 answers
137
GATE CSE 2021 Set 1 | Question: 20
Consider the following expression.$\displaystyle \lim_{x\rightarrow-3}\frac{\sqrt{2x+22}-4}{x+3}$The value of the above expression (rounded to 2 decimal places) is ___________.
Consider the following expression.$$\displaystyle \lim_{x\rightarrow-3}\frac{\sqrt{2x+22}-4}{x+3}$$The value of the above expression (rounded to 2 decimal places) is ____...
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3 votes
1 answer
138
GATE Overflow Test Series | Mock GATE | Test 4 | Question: 21
The minimum value of the function $f(x) = \frac{x^4}{4} - x^2 -3$ occurs at $x = 1$ $x =\sqrt 2$ $x = 0$ $ x = \frac{1}{\sqrt{4}}$
The minimum value of the function $$f(x) = \frac{x^4}{4} - x^2 -3$$ occurs at$x = 1$$x =\sqrt 2$$x = 0$$ x = \frac{1}{\sqrt{4}}$
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3 votes
2 answers
139
GATE Overflow Test Series | Mock GATE | Test 3 | Question: 59
If the function $f(x) =\left\{ \begin{array}{rcl} \alpha \sqrt{x+1} &;0\leq x \leq 3 \\\beta x + 2&;3 < x\leq 5\end{array}\right.$ is differentiable, then the value of $\alpha - \beta$ is _________
If the function $f(x) =\left\{ \begin{array}{rcl} \alpha \sqrt{x+1} &;0\leq x \leq 3 \\\beta x + 2&;3 < x\leq 5\end{array}\right.$ is differentiable, then the value of $\...
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0 votes
0 answers
142
TIFR-2018-Maths-A: 5
True/False Question : The function $f\left ( x \right )=cos\left ( e^{x} \right )$ is not uniformly continuous on $\mathbb{R}$.
True/False Question :The function $f\left ( x \right )=cos\left ( e^{x} \right )$ is not uniformly continuous on $\mathbb{R}$.
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3 votes
2 answers
143
NIELIT 2016 MAR Scientist C - Section B: 2
The function $f(x)=x^{5}-5x^{4}+5x^{3}-1$ has one minima and two maxima two minima and one maxima two minima and two maxima one minima and one maxima
The function $f(x)=x^{5}-5x^{4}+5x^{3}-1$ hasone minima and two maximatwo minima and one maximatwo minima and two maximaone minima and one maxima
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2 votes
1 answer
144
NIELIT 2016 MAR Scientist C - Section B: 10
$\underset{x \rightarrow 0}{\lim} \dfrac{x^{3}+x^{2}-5x-2}{2x^{3}-7x^{2}+4x+4}=?$ $-0.5$ $(0.5)$ $\infty$ None of the above
$\underset{x \rightarrow 0}{\lim} \dfrac{x^{3}+x^{2}-5x-2}{2x^{3}-7x^{2}+4x+4}=?$ $-0.5$$(0.5)$$\infty$None of the above
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1 votes
1 answer
145
NIELIT 2016 MAR Scientist C - Section B: 11
$\displaystyle \int_{0}^{\dfrac{\pi}{2}} \sin^{7}\theta \cos ^{4} \theta d\theta=?$ $16/1155$ $16/385$ $16\pi/385$ $8\pi/385$
$\displaystyle \int_{0}^{\dfrac{\pi}{2}} \sin^{7}\theta \cos ^{4} \theta d\theta=?$$16/1155$$16/385$$16\pi/385$$8\pi/385$
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1 votes
0 answers
146
NIELIT 2016 MAR Scientist C - Section B: 12
$\displaystyle \lim_{x \rightarrow a}\frac{1}{x^{2}-a^{2}} \displaystyle \int_{a}^{x}\sin (t^{2})dt=$? $2a \sin (a^{2})$ $2a$ $\sin (a^{2})$ None of the above
$\displaystyle \lim_{x \rightarrow a}\frac{1}{x^{2}-a^{2}} \displaystyle \int_{a}^{x}\sin (t^{2})dt=$?$2a \sin (a^{2})$$2a$$\sin (a^{2})$None of the above
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1 votes
2 answers
147
NIELIT 2016 MAR Scientist C - Section B: 13
$\displaystyle \lim_{x \rightarrow 0}\frac{1}{x^{6}} \displaystyle \int_{0}^{x^{2}}\frac{t^{2}dt}{t^{6}+1}=$? $1/4$ $1/3$ $1/2$ $1$
$\displaystyle \lim_{x \rightarrow 0}\frac{1}{x^{6}} \displaystyle \int_{0}^{x^{2}}\frac{t^{2}dt}{t^{6}+1}=$?$1/4$$1/3$$1/2$$1$
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