Engineering Maths · all questions

Calculus
practice.

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252

Questions

4/13

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Q61

The value of the integral of the function g(x, y) = 4x³ + 10y⁴ along the straight line segment from the point (0, 0) to the point (1, 2) in the x - y plane is

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Q62

The value of

x \to 0 lim \frac{1 - cos ( x ^{2} )}{2 x ^{4}}

is

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Q63

Consider points P and Q in the x-y plane, with P = (1, 0) and Q = (0, 1). The line integral

2 P \int Q (xdx + ydy)

along the semicircle with the line segment PQ as its diameter

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Q64

A surface S(x, y) = 2x + 5y - 3 is integrated once over a path consisting of the points that satisfy (x + 1)² + (y - 1)² = √2. The integral evaluates to

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Q65

Let w = f(x, y), where x and y are functions of t. Then, according to the chain rule,

\frac{dw}{dt}

is equal

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Q66

For the parallelogram OPQR shown in the sketch,

OP = a t^+ b j^

and

OR = c t^+ d j^.

The area of the parallelogram is
Calculus mcq question image

Calculus mcq question image

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Q67

The distance between the origin and the point nearest to it on the surface z² = 1 + xy is

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Q68

The value of

0 \int 3 0 \int x (6 - x - y) dx dy

is

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Q69

If for non-zero x,

af (x) + bf (\frac{1}{x}) = \frac{1}{x} - 25

where a ≠ b then

1 \int 2 f (x) dx

is

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Q70

The improper integral

0 \int \infty e^{- 2 t} dt

converges to

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Q71

As x increased from

- \infty

to

\infty

, the function

f (x) = \frac{e ^{x}}{1 + e ^{x}}

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Q72

The value of

x \to 1 lim \frac{x ^{7} - 2 x ^{5} + 1}{x ^{3} - 3 x ^{2} + 2}

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Q73

x \to 0 Lim \frac{x - sin x}{1 - cos x}

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Q74

Let f = y^x. What is

\frac{\partial ^{2} f}{\partial x \partial y}

at x = 2, y = 1?

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Q75

Given y = x² + 2x + 10, the value of

\frac{dy}{dx}_{x = 1}

is equal to

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Q76

A sphere of unit radius is centered at the origin. The unit normal at a point (x, y, z) on the surface of the sphere is the vector

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Q77

The total derivative of function xy is

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Q78

x \to 0 Lim (\frac{e ^{2 x} - 1}{sin ( 4 x )})

is equal to

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Q79

The value of the function

f (x) = x \to 0 lim \frac{x ^{3} + x ^{2}}{2 x ^{3} - 7 x ^{2}}

is

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Q80

Consider the function f(x) = |x|³, where x is real. Then the function f(x) at x = 0 is

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