Calculus of hyperbolic functions

Calculus of hyperbolic functions Quiz

Spec 8.2 · Edexcel A-Level Further Maths: Quiz

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5 questions, one answer each

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1. Differentiate $\cosh5x$ .
- A. $5\cosh5x$
- B. $5\sinh5x$
- C. $\sinh5x$
- D. $-5\sinh5x$
2. Differentiate $\tanh2x$ .
- A. $\frac{2}{\cosh^22x}$
- B. $\frac{1}{\cosh^22x}$
- C. $2\cosh^22x$
- D. $\frac{2}{\cosh2x}$
3. Find $\int\sinh4x\,dx$ .
- A. $4\cosh4x+c$
- B. $\frac14\sinh4x+c$
- C. $-\frac14\cosh4x+c$
- D. $\frac14\cosh4x+c$
4. Find the exact value of $\int_0^{\ln2}\cosh x\,dx$ .
- A. $\frac12$
- B. $\frac54$
- C. $\frac34$
- D. $\frac14$
5. Find $\int\frac{\cosh2x}{\sqrt{1+\sinh2x}}\,dx$ .
- A. $\frac12\sqrt{1+\sinh2x}+c$
- B. $\sqrt{1+\sinh2x}+c$
- C. $2\sqrt{1+\sinh2x}+c$
- D. $\frac{1}{\sqrt{1+\sinh2x}}+c$