Discuss the following situation by computation or proving. Make sure to show your complete solution. Give a polynomial division that has a quotient of x+5 and a remainder of -2.

left $f(x)=2^{\sin (x)}$
Find f'(x)

Decide if the equation represents exponential growth or decay. Explain your answer. $y=2^x/3^x$

a) Use base b = 10, precision k = 4, idealized, chopping floating-point arithmetic to show that fl(g(1.015)) is inaccurate, where ${\displaystyle g\left(x\right)=\frac{x^{\frac{1}{4}}-1}{x-1}}$ b) Derive the second order (n = 2) quadratic Taylor polynomial approximation for $f(x)=x^{\frac{1}{4}}$ expanded about a = 1, and use it to get an accurate approximation to g(x) in part (a). c) Verify that your approximation in (b) is more accurate.