step 1 the taylor polynomial with degree n = 3 is t3(x)=f(a)+f(a)(x - a)+f(a)2!(x - a)2+f(a)3!(x - a)3. the…

step 1 the taylor polynomial with degree n = 3 is t3(x)=f(a)+f(a)(x - a)+f(a)2!(x - a)2+f(a)3!(x - a)3. the function f(x)=e2x2 has derivatives f(x)=(4x)e2x2, f(x)=(4 + 16x2)e2x2, and f(x)=(48x + 64x3)e2x2. step 2 with a = 0, f(0)=, f(0)=, f(0)=, and f(0)=0. submit skip (you cannot come back) exercise (b) use taylors inequality to estimate the accuracy of the approximation f≈tn(x) when x lies in the given inte

step 1 the taylor polynomial with degree n = 3 is t3(x)=f(a)+f(a)(x - a)+f(a)2!(x - a)2+f(a)3!(x - a)3. the function f(x)=e2x2 has derivatives f(x)=(4x)e2x2, f(x)=(4 + 16x2)e2x2, and f(x)=(48x + 64x3)e2x2. step 2 with a = 0, f(0)=, f(0)=, f(0)=, and f(0)=0. submit skip (you cannot come back) exercise (b) use taylors inequality to estimate the accuracy of the approximation f≈tn(x) when x lies in the given inte

Answer

Explanation:

Step1: Evaluate f(0)

Substitute (x = 0) into (f(x)=e^{2x^{2}}). Since (e^{0}=1), then (f(0)=e^{2\times0^{2}} = 1).

Step2: Evaluate f'(0)

We know (f'(x)=4x e^{2x^{2}}). Substitute (x = 0) into (f'(x)), we get (f'(0)=4\times0\times e^{2\times0^{2}}=0).

Step3: Evaluate f''(0)

We know (f''(x)=(4 + 16x^{2})e^{2x^{2}}). Substitute (x = 0) into (f''(x)), we have (f''(0)=(4+16\times0^{2})e^{2\times0^{2}}=4).

Answer:

(f(0) = 1), (f'(0)=0), (f''(0)=4)