Tawjihiya Bahrain (Secondary School Certificate) · Advanced Mathematics

Calculus

32 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 32 questions

Let $f (x) = x^{3} + 5 x^{2} + x + 2$ . What is $f^{'} (1)$ ?
What is the equation of the tangent to the curve $y = - x^{2} + x + 4$ at the point where $x = - 1$ ?
Find $lim_{x \to \infty} \frac{5 x ^{2} + 10 x}{x ^{2} + 1}$ .
Evaluate $\int_{0}^{3} (6 x^{2} + 2) d x$ .
What is the equation of the vertical asymptote of $f (x) = \frac{5 x + 1}{x - 2}$ ?
For $f (x) = \frac{x ^{3}}{3} - 16 x$ , at which positive value of $x$ does $f$ have a local minimum?
What is the equation of the tangent to the curve $y = 2 x^{2} + 3 x + 4$ at the point where $x = - 1$ ?
Find $lim_{x \to \infty} \frac{2 x ^{2} + 5 x}{4 x ^{2} + 9}$ .
Evaluate $\int_{2}^{4} (2 x^{2} + 2) d x$ .
What is the equation of the vertical asymptote of $f (x) = \frac{2 x + 1}{x - 3}$ ?
For $f (x) = \frac{x ^{3}}{3} - 9 x$ , at which positive value of $x$ does $f$ have a local minimum?
Let $f (x) = 2 x^{3} + 2 x^{2} - x + 2$ . What is $f^{'} (2)$ ?
What is the equation of the tangent to the curve $y = 2 x^{2} - 2 x$ at the point where $x = 1$ ?
Evaluate $\int_{2}^{4} (6 x^{2} + 2) d x$ .
Let $f (x) = x^{3} + 3 x^{2} - 5 x + 7$ . What is $f^{'} (- 1)$ ?
Find $lim_{x \to \infty} \frac{3 x ^{2} + 2 x}{x ^{2} + 5}$ .
Evaluate $\int_{2}^{4} (3 x^{2} + 2) d x$ .
For $f (x) = \frac{x ^{3}}{3} - 4 x$ , at which positive value of $x$ does $f$ have a local minimum?
Let $f (x) = x^{3} - 4 x^{2} - 5 x + 7$ . What is $f^{'} (3)$ ?
Evaluate $\int_{1}^{3} (6 x^{2} + 6) d x$ .
What is the equation of the vertical asymptote of $f (x) = \frac{4 x + 3}{x - 5}$ ?
Let $f (x) = x^{3} + 3 x^{2} - 5 x - 3$ . 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 $lim_{x \to \infty} \frac{3 x ^{2} + 2 x}{3 x ^{2} + 7}$ .
Evaluate $\int_{2}^{4} (6 x^{2} + 6) d x$ .
Let $f (x) = x^{3} - 2 x^{2} + 4 x + 2$ . What is $f^{'} (1)$ ?
What is the equation of the tangent to the curve $y = 3 x^{2} - 4 x - 3$ at the point where $x = 1$ ?
Find $lim_{x \to \infty} \frac{2 x ^{2} + 5 x}{x ^{2} + 5}$ .
Let $f (x) = 3 x^{3} + 5 x^{2} + x - 3$ . What is $f^{'} (1)$ ?
What is the equation of the tangent to the curve $y = 2 x^{2} - 2 x - 3$ at the point where $x = 2$ ?
Find $lim_{x \to \infty} \frac{8 x ^{2} + 12 x}{2 x ^{2} + 1}$ .
Evaluate $\int_{1}^{3} (6 x^{2} + 2) d x$ .

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