help please

in Calculus Answers by Level 2 User (1.4k points)
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f(x) is wrongly defined because there is no x term in the definition. f(x)=e²ˣ? Or e^x²?

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I’m going to assume that f(x)=e²ˣ, so f(0.05)=1.10517...

df/dx=2e²ˣ, at x=a=0, df/dx=2, so the gradient for the linear approximation is 2. f(a)=f(0)=1.

L(x)=1+2x.

When x=0.05, L(0.05)=1+0.1=1.1.

Error is (f(0.05)-1.1)/f(0.05)=0.00468 or 0.47%.

[If I assume f(x)=e^x², df/dx=2xe^x²=0 when a=0, so L(x) would have no gradient, it would be a horizontal line. That means that the above assumption is probably correct.]

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