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Syllabus: Limits, Continuity, and Differentiability, Maxima and minima, Mean value theorem, Integration.

$$\scriptsize{\overset{{\large{\textbf{Mark Distribution in Previous GATE}}}}{\begin{array}{|c|c|c|c|c|c|c|c|}\hline
\textbf{Year}&\textbf{2024-1} &\textbf{2024-2} &\textbf{2023} &\textbf{2022} & \textbf{2021-1}&\textbf{2021-2}&\textbf{Minimum}&\textbf{Average}&\textbf{Maximum}
\\\hline\textbf{1 Mark Count} &1&1&2& 1 &1&1&1&1.16&2
\\\hline\textbf{2 Marks Count} &0&0&0& 0 &0&0&0&0&0
\\\hline\textbf{Total Marks} & 1&1&2&1 &1&1&\bf{1}&\bf{1.16}&\bf{2}\\\hline
\end{array}}}$$

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Hot questions in Calculus

3 votes
1 answer
421
Point of Inflexion
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1 votes
0 answers
422
Mathematics GATE 2018 CH: 54
The deacy ratio for a system having complex conjugate poles as $(-\dfrac{1}{10} + j\dfrac{2}{15})$ and $(-\dfrac{1}{10} - j\dfrac{2}{15})$ is $7\times10^{-1}$ $8\times10^{-2}$ $9\times10^{-3}$ $10\times10^{-4}$
The deacy ratio for a system having complex conjugate poles as$(-\dfrac{1}{10} + j\dfrac{2}{15})$ and $(-\dfrac{1}{10} - j\dfrac{2}{15})$ is$7\times10^{-1}$$8\times10^{-2...
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3 votes
1 answer
424
TIFR CSE 2018 | Part A | Question: 5
Which of the following is the derivative of $f(x)=x^{x}$ when $x>0$ ? $x^{x}$ $x^{x} \ln \;x$ $x^{x}+x^{x}\ln\;x$ $(x^{x}) (x^{x}\ln\;x)$ $\text{None of the above; function is not differentiable for }x>0$
Which of the following is the derivative of $f(x)=x^{x}$ when $x>0$ ?$x^{x}$$x^{x} \ln \;x$$x^{x}+x^{x}\ln\;x$$(x^{x}) (x^{x}\ln\;x)$$\text{None of the above; function is...
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2 votes
1 answer
425
Calculus Limit
Find the value of Here I got till $lim_{x \rightarrow \infty} \frac{4^2 + \frac{3^x}{4^x}}{4^{-2}}$. But how to proceed further?
Find the value of Here I got till $lim_{x \rightarrow \infty} \frac{4^2 + \frac{3^x}{4^x}}{4^{-2}}$. But how to proceed further?
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1 votes
1 answer
426
Maths: maxima and minima
In this maxima - minima question, teacher says that critical point -2 doesn't belong to the interval [-3, 3], isn't this wrong or i am missing something?
In this maxima - minima question, teacher says that critical point -2 doesn't belong to the interval [-3, 3], isn't this wrong or i am missing something?
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2 votes
1 answer
427
Limit question
$\lim_{x\rightarrow0}\frac{x^{2}+1}{x(x-1)}=?$
$\lim_{x\rightarrow0}\frac{x^{2}+1}{x(x-1)}=?$
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3 votes
0 answers
428
Maxima-Minima: ME GATE 2015
$At\ x\ =\ 0,\ the\ function\ f(x)\ =\ |x|\ has\ a\\ (a)Minimum\\(b)Maximum\\(c)a\ point\ of\ inflection\\(d)Neither\ a\ maxima\ nor\ a\ minima$
$At\ x\ =\ 0,\ the\ function\ f(x)\ =\ |x|\ has\ a\\ (a)Minimum\\(b)Maximum\\(c)a\ point\ of\ inflection\\(d)Neither\ a\ maxima\ nor\ a\ minima$
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2 votes
2 answers
429
Integration
$\int_{-4}^{4}\left | x-3 \right |dx$
$\int_{-4}^{4}\left | x-3 \right |dx$
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0 votes
0 answers
430
Differentiation confusion
Please show the steps how to differentiate u function equation and obtain this answer after differentating .please tell totally confused.
Please show the steps how to differentiate u function equation and obtain this answer after differentating .please tell totally confused.
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0 votes
2 answers
431
ISRO 2013- Integration [EE]
The integrating factor of equation sec 2 y dy/dx + x tan y = x3 is a) $[e]^{x^2/2}$ b) $[e]^ {-x^2/2}$ c) $[e]^{x/2}$ d)$ [e]^{-x/2}$
The integrating factor of equation sec 2 y dy/dx + x tan y = x3 isa) $[e]^{x^2/2}$b) $[e]^ {-x^2/2}$c) $[e]^{x/2}$d)$ [e]^{-x/2}$
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3 votes
1 answer
432
Calculus (LIMITS)
Answer is 1. I also know the procedure. My question is why isn't this formula working? Am I doing something wrong?
Answer is 1. I also know the procedure. My question is why isn't this formula working?Am I doing something wrong?
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4 votes
0 answers
433
Limits
What is the value of $\displaystyle \lim_{x\to \infty} \left(\frac{x}{2+x}\right)^{2x}?$
What is the value of $\displaystyle \lim_{x\to \infty} \left(\frac{x}{2+x}\right)^{2x}?$
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3 votes
1 answer
434
ISRO2016- EC Calculus
Evaluate $\int_0^1 \int_0^{\sqrt{1+x^2}} \frac{d x \cdot d y}{\left(1+x^2+y^2\right)}$ $\frac{\pi}{2}[\log (1+\sqrt{2})]$ $\frac{\pi}{4}[\log (1+\sqrt{2})]$ $\frac{\pi}{2}[\log (1-\sqrt{2})]$ $\frac{\pi}{4}[\log (1-\sqrt{2})]$
Evaluate $\int_0^1 \int_0^{\sqrt{1+x^2}} \frac{d x \cdot d y}{\left(1+x^2+y^2\right)}$$\frac{\pi}{2}[\log (1+\sqrt{2})]$$\frac{\pi}{4}[\log (1+\sqrt{2})]$$\frac{\pi}{2}[\...
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1 votes
0 answers
437
Integration area of curve
x 0 0.3 0.6 0.9 1.2 1.5 1.8 2.1 2.4 f(x) 0 0.09 0.36 0.81 1.44 2.25 3.24 4.41 5.76 The value of the below integral computed using the continuous at x = 3? $\int_{0}^{3} f(x) dx$ a) 8.983 b) 9.003 c) 9.017 d) 9.045
x00.30.60.91.21.51.82.12.4f(x)00.090.360.811.442.253.244.415.76The value of the below integral computed using the continuous at x = 3?$$\int_{0}^{3} f(x) dx$$a) 8.983b) 9...
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0 votes
0 answers
439
solve
$\sin x - \cos x > 0$ how to solve ?
$\sin x - \cos x 0$how to solve ?
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4 votes
5 answers
440
calculus problem on limits
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