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AP Calculus AB MCQ Question with Answer

AP Calculus AB MCQ with detailed explanation for interview, entrance and competitive exams. Explanation are given for understanding.

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Question No : 15
What does the definite integral ?(a to b) f(x) dx represent geometrically?

The average value of f(x) on [a, b]
The area between the curve y = f(x) and the x-axis on [a, b]
The derivative of f(x) at x = a
The slope of the tangent line to the curve y = f(x) at x = b
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Question No : 16
Which type of differential equation is represented by the equation dy/dx = k*y, where k is a constant?

Separable
Linear
Exact
Homogeneous
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Question No : 17
What is the directional derivative of the function f(x, y) = x^2 + y^2 at the point (1, 2) in the direction of the vector v = <3, 4>?

1
2
3
4
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Question No : 18
What is the distance between the points A(2, -1, 3) and B(4, 3, -2)?

v42
v30
v29
v35
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Question No : 19
What is the limit of (sin x) / x as x approaches 0?

1
0
-1
Undefined
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Question No : 20
What is the integral of e^(3x) with respect to x?

(1/3)e^(3x) + C
3e^(x) + C
(1/3)e^(x) + C
e^(3x) + C
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Question No : 21
What is the particular solution to the initial value problem dy/dx = 2x, y(0) = 1?

y = x^2 + 1
y = x^2
y = 2x + 1
y = 2x
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