Find the linear approximation of the function g(x)=(1+x)^(1/3) at a=0 and use it to approximate the numbers (0

Math Jan 25, 2021

Find the linear approximation of the function g(x)=(1+x)^(1/3) at a=0 and use it to approximate the numbers (0.95)^(1/3) and (1.1)^(1/3). Illustrate by graphing g and the tangent line.

Suppose that we don’t have a formula for g(x) but we know that g(2)= -4 and g‘(x)=(x^(2)+5)^(1/2) for all x. (a) use a linear approximation to estimate g(1.95) and g(2.05). (b) Are your estimates in part (a) too large or too small? Explain.

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