Engineering Maths · all questions

Calculus
practice.

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252

Questions

7/13

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Q121

Open question

The value of the integral

0 \int 2 \frac{( x - 1 ) ^{2} sin ( x - 1 )}{( x - 1 ) ^{2} + cos ( x - 1 )} dx

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Q122

Open question

Stokes theorem connects

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Q123

Open question

Which of the following integrals is unbounded?

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Q124

Open question

Changing the order of the integration in the double integral

I = 0 \int 8 \frac{x}{4} \int 2 f (x, y) dydx

leads to

I = r \int s p \int q f (x, y) dx dy .

What is q?

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Q125

Open question

The divergence of the vector field

A = x a^_{x} + y a^_{y} + z a^_{z}

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Q126

Open question

Compute

x \to 3 lim \frac{x ^{4} - 81}{2 x ^{2} - 5 x - 3}

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Q127

Open question

The angle (in degree) between two planes vectors

a = \frac{3}{2} i^+ \frac{1}{2} j^

and

b = \frac{- 3}{2} i^+ \frac{1}{2} j^

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Q128

Open question

The length of the curve

y = \frac{2}{3} x^{\frac{3}{2}}

between x = 0 and x = 1 is

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Q129

Open question

Consider the function f(x) = x² - x - 2. The maximum value of f(x) in the closed interval [-4, 4] is

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Q130

Open question

x \to 0 lim \frac{lo g _{e} ( 1 + 4 x )}{e ^{3 x} - 1}

is equal to

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Q131

Open question

What is the area common to the circles r = a and r = 2a cos θ?

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Q132

Open question

What should be the value of

λ

such that the function defined below is continuous at

x = \frac{π}{2} ?

{\text{f}}\left( {\text{x}} \right) = \left\{ {\begin{array}{*{20}{c}} {\frac{{\lambda \cos {\text{x}}}}{{\frac{\pi }{2} - {\text{x}}}}}&{{\text{if x}} \ne \frac{\pi }{2}} \\ 1&{{\text{if x}} = \frac{\pi }{2}} \end{array}} \right.

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Q133

Open question

For the function f(x) = x²e^-x, the maximum occurs when x is equal to

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Q134

Open question

The value of integral

- \frac{π}{2} \int \frac{π}{2} (x cos x) dx

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Q135

Open question

For the two functions, f(x, y) = x³ - 3xy² and g(x, y) = 3x²y - y², which one of the following options is correct?

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Q136

Open question

A function f(x) is continuous in the interval [0, 2]. It is known that f(0) = f(2) = -1 and f(1) = 1.
Which one of the following statements must be true?

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Q137

Open question

How many distinct values of x satisfy the equation sin(x) =

\frac{x}{2}

, where x is in radians?

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Q138

Open question

The

x \to 0 lim \frac{sin [ \frac{2}{3} x ]}{x}

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Q139

Open question

The value expression

x \to 0 lim \frac{sin x}{e ^{x} x}

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Q140

Open question

Assuming

i = - 1

and t is a real number,

0 \int \frac{π}{3} e^{it} dt

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Calculus
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