Državna Matura (Montenegro) · Mathematics (State Matura Montenegro)

Calculus

23 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 23 questions

Let $f (x) = 2 x^{3} + 5 x^{2} + 4 x + 7$ . What is $f^{'} (3)$ ?
Find $lim_{x \to \infty} \frac{4 x ^{2} + 3 x}{4 x ^{2} + 9}$ .
Evaluate $\int_{0}^{2} (3 x^{2} + 2) d x$ .
What is the equation of the vertical asymptote of $f (x) = \frac{5 x + 1}{x - 2}$ ?
Let $f (x) = 3 x^{3} + 3 x^{2} + x - 3$ . What is $f^{'} (3)$ ?
What is the equation of the tangent to the curve $y = - x^{2} + 3 x$ at the point where $x = - 1$ ?
Find $lim_{x \to \infty} \frac{6 x ^{2} + 4 x}{2 x ^{2} + 1}$ .
Evaluate $\int_{0}^{2} (2 x^{2} + 3) d x$ .
What is the equation of the vertical asymptote of $f (x) = \frac{2 x + 1}{x - 3}$ ?
For $f (x) = \frac{x ^{3}}{3} - 16 x$ , at which positive value of $x$ does $f$ have a local minimum?
Let $f (x) = 3 x^{3} - 3 x^{2} + 4 x - 3$ . What is $f^{'} (3)$ ?
What is the equation of the tangent to the curve $y = x^{2} + 5 x + 4$ at the point where $x = 2$ ?
Find $lim_{x \to \infty} \frac{6 x ^{2} + 4 x}{x ^{2} + 1}$ .
Evaluate $\int_{2}^{4} (2 x^{2} + 3) d x$ .
What is the equation of the vertical asymptote of $f (x) = \frac{1 x + 4}{x - 2}$ ?
For $f (x) = \frac{x ^{3}}{3} - 9 x$ , at which positive value of $x$ does $f$ have a local minimum?
Let $f (x) = 3 x^{3} - 3 x^{2} + x + 2$ . What is $f^{'} (1)$ ?
Find $lim_{x \to \infty} \frac{6 x ^{2} + 4 x}{3 x ^{2} + 7}$ .
Evaluate $\int_{0}^{2} (x^{2} + 2) d x$ .
For $f (x) = \frac{x ^{3}}{3} - 4 x$ , at which positive value of $x$ does $f$ have a local minimum?
Find $lim_{x \to \infty} \frac{5 x ^{2} + 10 x}{3 x ^{2} + 7}$ .
Evaluate $\int_{0}^{2} (2 x^{2} + 2) d x$ .
What is the equation of the vertical asymptote of $f (x) = \frac{4 x + 3}{x - 5}$ ?

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