Engineering Maths · all questions

Calculus
practice.

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252

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Q181

Open question

f (x) = sin ∣ x ∣

then value of

\frac{df}{dx}

x = \frac{- π}{4}

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Q182

Open question

The value of integral

S \int \int ◯ r \cdot n ds

over the closed surface S bounding a volume, where

r = x i^+ y j^+ z k^

is the position vector and

\frac{\buildrel \lower 3pt ⇀}{n}

is the normal to the surface S, is

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Q183

Open question

Which of the following statements are correct regarding dot product of vectors?
1. Dot product is less than or equal to the product of magnitudes of two vectors.
2. When two vectors are perpendicular to each other, then their dot product is non-zero.
3. Dot product of two vectors is positive or negative depending whether the angle between the vectors is less than or greater than

\frac{π}{2}

.
4. Dot product is equal to the product of one vector and the projection of the vector on the first one.
Select the correct answer:

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Q184

Open question

The volume of the solid surrounded by the surface

(\frac{x}{a})^{\frac{2}{3}} + (\frac{y}{b})^{\frac{2}{3}} + (\frac{z}{c})^{\frac{2}{3}} = 1

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Q185

Open question

For the function, f(x, y) = x² - y² defined on R², the point (0, 0) is

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Q186

Open question

A path AB in the form of one quarter of a circle of unit radius is shown in the figure. Integration of (x + y)² on path AB traversed in a counterclockwise sense is
Calculus mcq question image

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Q187

Open question

The minimum value of the function f(x) = x³ - 3x² - 24x + 100 in the interval [-3, 3] is

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Q188

Open question

The directional derivative of f(x, y, z) = 2x² + 3y² + z² at the point P(2, 1, 3) in the direction of the vector a = i - 2k is

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Q189

Open question

What is the value of

n \to \infty lim (1 - \frac{1}{n})^{2 n} ?

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Q190

Open question

The line integral of function F = yzi, in the counter-clockwise direction, along the circle x² + y² = 1 at z = 1 is

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Q191

Open question

Minimum of the real valued function

f (x) = (x - 1)^{\frac{2}{3}}

occurs at x equal to

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Q192

Open question

Given the following statements about a function f : R → R , select the right option:
P: If f(x) is continuous at x = x₀, then it is differential at x = x₀.
Q: If f(x) is continuous at x = x₀, then it may not be differentiable at x = x₀.
R: If f(x) is differentiable at x = x₀, then it is also continuous at x = x₀.

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Q193

Open question

The integral