Engineering Maths · all questions

Calculus
practice.

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252

Questions

9/13

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Q161

What is curl of the vector field 2x²yi + 5z²j - 4uyzk?

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Q162

A rail engine accelerates from its stationary position for 8 seconds and travels a distance of 280 m. According to the Mean Value Theorem, the speedometer at a certain time during acceleration must read exactly

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Q163

Let f(x) = x e^-x. The maximum value of the function in the interval (0,

\infty

) is

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Q164

The contour on the x - y plane, where the partial derivative of x² + y² with respect to y is equal to the partial derivative of 6y + 4x with respect to x, is

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Q165

Consider the following equations

\frac{\partial V ( x, y )}{\partial x} = p x^{2} + y^{2} + 2 xy \hfill \frac{\partial V ( x, y )}{\partial y} = x^{2} + q y^{2} + 2 xy \hfill

where p and q are constants. V(x, y) that satisfies the above equations is

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Q166

x \to 0 lim \frac{e ^{x} - ( 1 + x + \frac{x ^{2}}{2} )}{x ^{3}} = ?

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Q167

The quadratic approximation of f(x) = x³ - 3x² - 5 a the point x = 0 is

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Q168

The following inequality is true for all x close to 0.

2 - \frac{x ^{2}}{3} < \frac{x sin x}{1 - cos x} < 2

What is the value of

x \to 0 lim \frac{x sin x}{1 - cos x} ?

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Q169

The series

n = 0 \sum \infty \frac{1}{n !}

converges to

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Q170

The quadratic approximation of f(x) = x³ - 3x² - 5 a the point x = 0 is

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Q171

If

f (x) = R sin (\frac{π x}{2}) + S, f^{'} (\frac{1}{2}) = 2

and

0 \int 1 f (x) dx = \frac{2 R}{π},

then the constants R and S are, respectively

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Q172

The vector function

A

is given by

A = \nabla u,

where u(x, y) is a scalar function, Then

\nabla \times A

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Q173

If

u = lo g (\frac{x ^{2} + y ^{2}}{x + y}),

what is the value of

x \frac{\partial u}{\partial x} + y \frac{\partial u}{\partial y} ?

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Q174

Consider the plot f(x) versus x as shown below
Calculus mcq question image

Calculus mcq question image

Suppose

F (x) = \int_{- 5}^{x} f (y) dy .

Which one of the following is a graph of F(x)?

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Q175

Consider the following definite integral:

I = 0 \int 1 \frac{( sin ^{- 1} x ) ^{2}}{1 - x ^{2}} dx

The value of the integral is

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Q176

The value of the directional derivative of the function

ϕ

(x, y, z) = xy² + yz² + zx² at the point (2, -1, 1) in the direction of the vector p = i + 2j + 2k is

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Q177

Which one of the following graphs describes the function f(x) = e^-x(x² + x + 1)?

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Q178

0 \int \frac{π}{4} \frac{( 1 - tan x )}{( 1 + tan x )} dx

evaluates to

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Q179

Divergence of the three-dimensional radial vector field

r

is

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Q180

In the Taylor series expansion of exp(x) + sin(x) about the point x = π, the coefficient of (x - π)² is

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