Engineering Maths · all questions

Calculus
practice.

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Q81

Open question

The integral

0 \int π sin^{3} θ d θ

is given by

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Q82

Open question

The volume of an object expressed in spherical co-ordinates is given by

V = \int_{0}^{2 π} \int_{0}^{\frac{π}{3}} \int_{0}^{1} r^{2} sin ϕ dr d ϕ d θ .

The value of the integral is

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Q83

Open question

The value of the integral

\int_{0}^{\infty} \int_{0}^{\infty} e^{- x^{2}} e^{- y^{2}} dx dy

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Q84

Open question

The range of value of k for which the function f(x) = (k² - 4)x² + 6x³ + 8x⁴ has a local maxima at point x = 0 is

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Q85

Open question

The area of the region bounded by the parabola y = x² + 1 and the straight line x + y = 3 is

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Q86

Open question

The maximum value of f(x) = x³ - 9x² + 24x + 5 in the interval [1, 6] is

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Q87

Open question

The value of the integral

\int_{0}^{2 π} (\frac{3}{9 + sin ^{2} θ}) d θ

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Q88

Open question

A velocity vector is given as

V = 5 xy i + 2 y^{2} j + 3 y z^{2} k .

The divergence of this velocity vector at (1, 1, 1) is

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Q89

Open question

Given a vector field

F = y^{2} x a^_{x} - yz a^_{y} - x^{2} a^_{z},

the line integral

\int F \cdot d l

evaluated along a segment on the x-axis from x = 1 to x = 2 is

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Q90

Open question

At the point x = 0, the function f(x) = x³ has

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Q91

Open question

Let f be a real-valued function of a real variable defined as f(x) = x² for x ≥ 0, and f(x) = -x² for x < 0. Which one of the following statements is true?

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Q92

Open question

The value of

x \to \infty lim (1 + \frac{1}{x})^{x}

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Q93

Open question

The divergence of the vector field

U = e^{x} (cos y i^+ sin y j^)

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Q94

Open question

Given a function f(x, y) = 4x² + 6y² - 8x - 4y + 8. The optimal value of f(x, y)

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Q95

Open question

To evaluate the double integral

\int_{0}^{8} (\int_{\frac{y}{2}}^{\frac{y}{2} + 1} (\frac{2 x - y}{2}) dx) dy,

we make the substitution

u = \frac{2 x - y}{2}

and

v = \frac{y}{2} .

The integral will reduce to

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Q96

Open question

\iint (\nabla \times P) \cdot ds,

where P is a vector, is equal to

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Q97

Open question

x \to 0 Lim \frac{sin x}{x}

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Q98

Open question

At t = 0, the function

f (t) = \frac{sin t}{t}

has

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Q99

Open question

A point on a curve is said to be an extremum if it is a local minimum or a local maximum. The number of distinct extrema for the curve 3x⁴ - 16x³ - 24x² + 37 is

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Q100

Open question

If P, Q and R are three points having coordinates (3, -2, -1), (1, 3, 4), (2, 1, -2) in XYZ space, then the distance from point P to plane OQR (O being the origin of the coordinate system) is given by

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Calculus
practice.