Calculus with hyperbolic functions

Calculus with hyperbolic functions Quiz

Spec H2 · AQA A-Level Further Maths: Quiz

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5 questions, one answer each

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1. Differentiate $\sinh 5x$ .
- A. $\cosh 5x$
- B. $5\cosh 5x$
- C. $\frac15\cosh 5x$
- D. $-5\cosh 5x$
2. Find $\int\operatorname{sech}^2 3x\,dx$ .
- A. $\frac13\tanh 3x+c$
- B. $3\tanh 3x+c$
- C. $\tanh 3x+c$
- D. $\frac13\operatorname{sech}3x+c$
3. Differentiate $\ln(\cosh x)$ .
- A. $\operatorname{sech}x$
- B. $\coth x$
- C. $\frac{1}{\sinh x}$
- D. $\tanh x$
4. Find $\int_0^{\ln3}\sinh x\,dx$ .
- A. $\frac13$
- B. $\frac23$
- C. $\frac43$
- D. $\frac53$
5. Find $\int\frac{1}{\sqrt{x^2+25}}\,dx$ .
- A. $\operatorname{arcosh}\frac x5+c$
- B. $\frac15\operatorname{arsinh}\frac x5+c$
- C. $\operatorname{arsinh}\frac x5+c$
- D. $\frac15\operatorname{arcosh}\frac x5+c$