The approximation $(1+x)^k\approx 1+kx$ is commonly used by engineers for quick calculations.

(a) Derive this result and use it to make a rough estimate of $(1.01)^{37}$.

$(1.01)^{37}\approx$ Enter value to 6 decimal places.

(b) The error between the computed and estimated values of $(1+x)^k$ is given by; $$E(x)=|(1+x)^k-(1+kx)|$$ Using your answer to part (a) compute $E(1.01)$ to 6 decimal places.

$E(1.01)$ =