What is taylor e^{2x},3 ?

The answer to taylor e^{2x},3 is e^6+2e^6(x-3)+2e^6(x-3)^2+(4e^6)/3 (x-3)^3+(2e^6)/3 (x-3)^4+\ldots

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taylor e^{2x},3

taylor

e^{2 x}, 3

e^{6} + 2 e^{6} (x - 3) + 2 e^{6} (x - 3)^{2} + \frac{4 e ^{6}}{3} (x - 3)^{3} + \frac{2 e ^{6}}{3} (x - 3)^{4} + \dots

Solution steps

Apply the Taylor Formula

= e^{6} + \frac{\frac{d}{d x} ( e ^{2 x} ) ( 3 )}{1 !} (x - 3) + \frac{\frac{d ^{2}}{d x ^{2}} ( e ^{2 x} ) ( 3 )}{2 !} (x - 3)^{2} + \frac{\frac{d ^{3}}{d x ^{3}} ( e ^{2 x} ) ( 3 )}{3 !} (x - 3)^{3} + \dots

Evaluate Derivatives

= e^{6} + \frac{2 e ^{6}}{1 !} (x - 3) + \frac{4 e ^{6}}{2 !} (x - 3)^{2} + \frac{8 e ^{6}}{3 !} (x - 3)^{3} + \frac{16 e ^{6}}{4 !} (x - 3)^{4} + \dots

Refine

= e^{6} + 2 e^{6} (x - 3) + 2 e^{6} (x - 3)^{2} + \frac{4 e ^{6}}{3} (x - 3)^{3} + \frac{2 e ^{6}}{3} (x - 3)^{4} + \dots

\int \frac{4 x ^{2} + 6}{( x ^{2} - 2 x + 2 ) ^{2}} d x

\int sin^{5} (θ) cos^{5} (θ) d θ

x + 2, - 3 x + 6, 0, 1

\frac{d}{d x} (- 9 cos (x))

\frac{\partial}{\partial x} (x^{2} + y^{2} + x y)

What is taylor e^{2x},3 ?
The answer to taylor e^{2x},3 is e^6+2e^6(x-3)+2e^6(x-3)^2+(4e^6)/3 (x-3)^3+(2e^6)/3 (x-3)^4+\ldots