Recent questions tagged calculus

Given two complex numbers $z_1=5+(5\sqrt{3})i$ and $z_2=\dfrac{2}{\sqrt{3}}+2i$ , the argument of $\dfrac{z_1}{z_2}$ in degrees is$0$$30$$60$$90$

The value of $\displaystyle{} \lim_{x\rightarrow 0}\dfrac{1- \cos(x^2)}{2x^4}$ is$0 \\$$\dfrac{1}{2} \\$$\dfrac{1}{4} \\$undefined

Consider a velocity field $\overrightarrow{V}=k(y\hat{i}+x\hat{k})$ , where $K$ is a constant. The vorticity, $Ω_Z$ , is$-K$$K$$-K/2$$K/2$

The value of the integral $\int_{0}^{2}\int_{0}^{x}e^{x+y}dydx$ is$\dfrac{1}{2}(e-1) \\$$\dfrac{1}{2}(e^2-1)^2 \\$$\dfrac{1}{2}(e^2-e) \\$$\dfrac{1}{2}(e-\frac{1}{e})^2$

If $z$ is a complex variable, the value of $\displaystyle{} \int_{5}^{3i}\dfrac{dz}{z}$ is$− 0.511−1.57i$$− 0.511+1.57i$$0.511− 1.57i$$0.511+1.57i$

The value of the integral $$\int_{0}^{2}\dfrac{(x-1)^2\sin(x-1)}{(x-1)^2+\cos(x-1)}dx$$ is$3$$0$$-1$$-2$

An analytic function of a complex variable $z = x + i y$ is expressed as $f (z) = u(x, y) + i v(x, y)$ , where $i=\sqrt{-1}$ . If $u(x, y) = x^2 − y^2$ , then expression...

The real root of the equation $5x − 2 \cos x −1 = 0$ (up to two decimal accuracy) is _______

Divergence of the vector field $x_2z\hat{i}+xy\hat{j}-yz\hat{k}$ at $(1,-1,1)$ is$0$$3$$5$$6$

An analytic function of a complex variable $z=x+iy$ is expressed as $f(z)=u(x,y)+iv(x,y)$ , where $i=\sqrt{-1}$ If $u(x,y)=2xy$, then $v(x,y)$ must be$x^2$+$y^2$+constant...

Curl of vector $\overrightarrow{F}=x^2z^2\hat{i}-2xy^2z\hat{j}+2y^2z^3\hat{k}$ is$(4yz^3+2xy^2)\hat{i}+2x^2z\hat{j}-2y^2z\hat{k}$$(4yz^3+2xy^2)\hat{i}-2x^2z\hat{j}-2y^2z\...

$ \displaystyle{}\lim_{x\rightarrow 0} \left( \dfrac{e^{2x}-1}{\sin(4x)} \right )$ is equal to$0$$0.5$$1$$2$

If $y = f(x)$ is the solution of $\dfrac{d^2y}{dx^2}=0$ with the boundary conditions y = $5$ at $x = 0$ and $\dfrac{dy}{dx}=2$ at $x = 10$, $f(15) =$ _____________ .

The integral $\oint_{c}^{ } (ydx-xdy)$ is evaluated along the circle $x^2+y^2=\frac{1}{4}$ traversed in counter clockwise direction. The integral is equal to$0$$\frac{-\p...

The argument of the complex number $\dfrac{1+\imath }{1-\imath }$ where $\imath =\sqrt{-1}$ ,isA. $-\pi$B. $\dfrac{-\pi }{2}$C. $\dfrac{\pi }{2}$ D. $\pi$

$\displaystyle{} \lim_{x\rightarrow 0}\dfrac{x- \sin x}{1- \cos x}$ is$0$$1$$3$not defined

The value of the definite integral $\int_{1}^{e}\sqrt{x}\ln(x)dx$ is$\dfrac{4}{9}\sqrt{e^3}+\dfrac{2}{9} \\$$\dfrac{2}{9}\sqrt{e^3}-\dfrac{4}{9} \\$$\dfrac{2}{9}\sqrt{e^3...

The following surface integral is to be evaluated over a sphere for the given steady velocity vector field $F$ = $xi$ + $yj$+ $zk$ defined with respect to a Cartesian coo...

Choose the CORRECT set of functions, which are linearly dependent.$\sin x , \sin^2 x$ and $\cos^2 x$$\cos x , \sin x$ and $\tan x$$\cos 2x, \sin^2 x$ and $\cos^2 x$$\cos ...