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Calculus
practice.

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252

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Q21

Open question

The value of the quantity P, where

P = 0 \int 1 x e^{x} dx,

is equal to

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Q22

Open question

What is the value of

x \to \frac{π}{4} lim \frac{cos x - sin x}{x - \frac{π}{4}}

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Q23

Open question

The value of

x \to \infty lim (1 + x^{2})^{e^{- x}}

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Q24

Open question

For a right angled triangle, if the sum of the lengths of the hypotenuse and a side is kept constant, in order to have maximum area of the triangle, the angle between the hypotenuse and the side is

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Q25

Open question

The value of

x \to 8 lim \frac{x ^{\frac{1}{3}} - 2}{( x - 8 )}

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Q26

Open question

The vector that is NOT perpendicular to the vectors (i + j + k) and (i + 2j + 3k) is . . . . . . . .

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Q27

Open question

Given

i = - 1,

what will be the evaluation of the definite integral

\int_{0}^{\frac{π}{2}} \frac{cos x + i sin x}{cos x - i sin x} dx ?

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Q28

Open question

At x = 0, the function

f (x) = sin \frac{2 π x}{L}

, (-

\infty

< x <

\infty

, L > 0) is

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Q29

Open question

The value of

\int_{0}^{\infty} \frac{1}{1 + x ^{2}} dx + \int_{0}^{\infty} \frac{sin x}{x} dx

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Q30

Open question

The values of the integrals

0 \int 1 0 \int 1 \frac{x - y}{( x + y ) ^{3}} dy dx

and

0 \int 1 0 \int 1 \frac{x - y}{( x + y ) ^{3}} dx dy

are

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Q31

Open question

a, b, c

are three orthogonal vectors, Given that

a = i^+ 2 j^+ 5 k^

and

b = i^+ 2 j^- k^

, the vector

c

is parallel to

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Q32

Open question

Given

F = (x^{2} - 2 y) i - 4 yz j + 4 x z^{2} k,

the value of the line integral

c \int F \cdot d l

along the straight line c from (0, 0, 0) to (1,1,1) is

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Q33

Open question

At x = 0, the function f(x) = |x| has

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Q34

Open question

A parabola x = y² with 0 ≤ x ≤ 1 is shown in the figure. The volume of the solid of rotation obtained by rotating the shaded area by 360° around the x-axis is
Calculus mcq question image

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Q35

Open question

The line integral

P_{1} \int P_{2} (ydx + xdy)

for P₁(x₁, y₁) to P₂(x₂, y₂) along the semicircle P₁, P₂ shown in the figure is
Calculus mcq question image

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Q36

Open question

The angle between two unit-magnitude coplanar vectors P(0.866, 0.500, 0) and Q(0.259, 0.966, 0) will be

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Q37

Open question

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 coordinate system having i, j and k as unit base vectors.

S \iint \frac{1}{4} (F \cdot n) dA

where S is the sphere, x² + y² + z² = 1 and n is the outward unit normal vector to the sphere.
The value of the surface integral is

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Q38

Open question

If a function is continuous at a point,

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Q39

Open question

The vector that is normal to the surface 2xz² - 3xy - 4x = 7 at the point (1, -1, 2) is

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Q40

Open question

The derivative of the symmetric function drawn in given figure will look like
Calculus mcq question image

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Calculus
practice.