If y=(x+1)(x2+1)(x4+1)(x8+1), then displaystyle lim x arrow-1 (d y/d x)=

Question

If y=(x+1)(x2+1)(x4+1)(x8+1), then displaystyle lim x arrow-1 (d y/d x)= (A) 0 (B) 2 (C) -4 (D) 8

Tardigrade Admin · Accepted Answer

We have, y=(x+1)(x2+1)(x4+1)(x8+1) (d y/d x)=(x2+1)(x4+1)(x8+1)+2 x(x+1)(x4+1) (x8+1)+4 x3(x+1)(x2+1)(x8+1)+8 x7(x+1) (x2+1)(x4+1) ((d y/d x))x=-1=(1+1)(1+1)(1+1)+0+0+0=8

Q. If y=(x+1)(x2+1)(x4+1)(x8+1), then x→−1lim​dxdy​=

0

2

-4

8

We have, y=(x+1)(x2+1)(x4+1)(x8+1) dxdy​=(x2+1)(x4+1)(x8+1)+2x(x+1)(x4+1) (x8+1)+4x3(x+1)(x2+1)(x8+1)+8x7(x+1)(x2+1)(x4+1) (dxdy​)x=−1​=(1+1)(1+1)(1+1)+0+0+0=8

Q. If $y = (x + 1) (x^{2} + 1) (x^{4} + 1) (x^{8} + 1)$ , then $x \to - 1 lim \frac{d y}{d x} =$