Recent questions tagged calculus

Consider the following infinite series:$$1+ r+r^2 +r^3+ \dots \dots \infty$$ If $r = 0.3$, then the sum of this infinite series is ____________

The limit of the function $\bigg (1 + \dfrac{x}{n} \bigg )^n$ as $n \to \infty$ is$\ln x$$\ln \dfrac{1}{x}$$e^{-x}$$e^x$

The limit of the function $e^{-2t}\sin (t)$ as t $\rightarrow\infty$ so, is

The concentration profile of a chemical at a location $x$ and time $t$, denoted by $c(x,t)$, changes as per the following equation,$$c(x,t)=\frac{c_0}{\sqrt{2\pi Dt}}\exp...

If $y =x^x$, then $\frac{dy}{dx}$ is$x^x(x-1)$$x^{x-1}$$x^x(1 + \log x)$$e^x(1 + \log x)$

Which of the following statements is true for the series given below?$$S_n=1+\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{3}}+\frac{1}{\sqrt{4}}+\dots+\frac{1}{\sqrt{n}} $$$S_n$ con...

The graph of the function $F(x) =\frac{x}{k_1x^2+k_2x+1}$ for $0<x<\infty$ is

The solution to $\frac {dy}{dx}+y \cot x=\csc x$ is$y=(c+x)\cot x$$y=(c+x)\csc x$$y=(c+x)\csc x\cot x$$y=(c+x)\frac{\csc x}{\cot x}$

Evaluate $\underset{x\rightarrow\infty }{\lim}x\tan\frac{1}{x}$$\infty$$1$$0$$-1$

If $u=\log (e^x+e^y),$ then $\frac{\partial u}{\partial x}+\frac{\partial u}{\partial y}=$$e^x+e^y$$e^x-e^y$$\frac{1}{e^x+e^y}$$1$

If $1+r + r^2+ r^3 +\dots \infty = 1.5$, then, $1 + 2r + 3r^2 + 4r^3 + \dots \infty = $ (up to two dcimal places) ________

Calculate the following integral (up to two decimal places)$$\displaystyle \int_0^1 (x + 3)(x + 1)dx = \text{ ___________}$$

Which one of the following is the solution for $\cos^2 x + 2 \cos x + 1 = 0$, for values of $x$ in the range of $0^\circ < x < 360^\circ$$45^\circ$$90^\circ$$180^\circ$$2...