German Abitur · Mathematics

Analysis: Calculus

25 practice questions, each with the answer and an explanation.

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Random questions from this topic, one at a time. You see the answer and the explanation straight after each one.

All 25 questions

What is the derivative of $f (x) = x^{4} - 2 x^{2} + 5$ at $x = 1$ ?
What is the value of $\int_{0}^{2} 3 x^{2} d x$ ?
What are the zeros of $f (x) = x^{2} - 5 x + 6$ ?
For $f (x) = x^{3} - 6 x^{2} + 9 x$ , at which $x$ does the graph have a local maximum?
What is the equation of the tangent to $f (x) = x^{2}$ at the point where $x = 3$ ?
What is the area enclosed between the graphs of $f (x) = x$ and $g (x) = x^{2}$ for $0 \leq x \leq 1$ ?
What is the derivative of $f (x) = x \cdot e^{x}$ ?
A rectangle has a perimeter of $40$ cm. What is the largest area it can have?
What is $lim_{x \to \infty} \frac{2 x ^{2} + 3 x}{x ^{2} - 1}$ ?
What is $\int cos (2 x) d x$ ?
What is the derivative of $f (x) = sin (x^{2})$ ?
Where does $f (x) = x^{3} - 6 x^{2} + 9 x$ have its inflection point?
For which $x$ does $f (x) = \frac{l n x}{x}$ (with $x > 0$ ) attain its maximum?
For which values of $a$ does $f_{a} (x) = x^{3} - a x$ have exactly two local extrema?
What is the mean value of $f (x) = x^{2}$ on the interval $[0, 3]$ ?
What is the value of the improper integral $\int_{1}^{\infty} \frac{1}{x ^{2}} d x$ ?
Let $f (x) = 2 x^{3} + 2 x^{2} + x$ . What is the slope of the tangent at $x = 0$ ?
Let $f (x) = 3 x^{3} + 2 x$ . What is the slope of the tangent at $x = - 2$ ?
Let $f (x) = 4 x^{3} + 5 x^{2} + 3 x$ . What is the slope of the tangent at $x = 2$ ?
Let $f (x) = 4 x^{3} + 4 x^{2} - 2 x$ . What is the slope of the tangent at $x = - 2$ ?
Compute $\int_{0}^{2} (1 x^{2} + 5) d x$ .
Compute $\int_{0}^{4} (3 x^{2} + 0) d x$ .
Compute $\int_{0}^{4} (1 x^{2} + 5) d x$ .
What is the derivative of $f (x) = e^{2 x}$ ?
What is the derivative of $f (x) = e^{4 x}$ ?

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Analysis: Calculus

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