Find the quadratic approximation of f at x = 0.
-f(x) = sin ln(8x + 1)
A) $Q ( x ) = 1 + 8 x + 32 x ^ { 2 }$
B) $Q ( x ) = 8 x - 32 x ^ { 2 }$
C) $Q ( x ) = 8 x + 32 x ^ { 2 }$
D) $Q ( x ) = 1 - 8 x + 32 x ^ { 2 }$

Question

Find the quadratic approximation of f at x = 0.
-f(x) = sin ln(8x + 1) 
A) $Q ( x ) = 1 + 8 x + 32 x ^ { 2 }$
B) $Q ( x ) = 8 x - 32 x ^ { 2 }$
C) $Q ( x ) = 8 x + 32 x ^ { 2 }$
D) $Q ( x ) = 1 - 8 x + 32 x ^ { 2 }$

Quizplus · Accepted Answer

The quadratic approximation of a function f at x = 0 is given by $ f(0) + f'(0)x + \frac{f''(0)}{2}x^2 $. For $ f(x) = \sin(\ln(8x + 1)) $, $ f(0) = 0 $, $ f'(0) = 8 $, and $ f''(0) = -64 $. Thus, the quadratic approximation is $ 8x - 32x^2 $.

Find the Quadratic Approximation of F at X = 0 Q(x)=1+8x+32x2Q ( x ) = 1 + 8 x + 32 x ^ { 2 }Q(x)=1+8x+32x2

Find the Quadratic Approximation of F at X = 0 $Q ( x ) = 1 + 8 x + 32 x ^ { 2 }$