Calculus 1st Semester Review

Calculus 1st Semester Review

Assessment

Flashcard

Mathematics

11th Grade - University

Practice Problem

Hard

Created by

Wayground Content

FREE Resource

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15 questions

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1.

FLASHCARD QUESTION

Front

What is the derivative of A = 2x^3 with respect to time t?

Back

dA/dt = 6x^2 (dx/dt)

2.

FLASHCARD QUESTION

Front

If the radius of an oil spill increases at a rate of 5 m/min, how do you find the rate at which the area of the spill is increasing?

Back

Area A = πr^2; dA/dt = 2πr(dr/dt). When r = 5 m, dA/dt = 50π m²/min.

3.

FLASHCARD QUESTION

Front

What does it mean if f''(x) > 0 over an interval?

Back

It means that f'(x) is increasing over that interval.

4.

FLASHCARD QUESTION

Front

Find the second derivative of f(x) = x^2 + e^x - cos(x).

Back

f''(x) = 2 + e^x + sin(x)

5.

FLASHCARD QUESTION

Front

At what point does a bug change direction if its velocity function is given?

Back

The bug changes direction at t = 6.5.

6.

FLASHCARD QUESTION

Front

What is the chain rule in calculus?

Back

If y = f(g(x)), then dy/dx = f'(g(x)) * g'(x).

7.

FLASHCARD QUESTION

Front

Define the concept of limits in calculus.

Back

A limit is the value that a function approaches as the input approaches a certain point.

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