If f(x) = 3x10 - 7x8 + 5x6 - 21x3 + 3x2 - 7, then displaystyle limα → 0(f(1-α)-f (1)/α3+3α) is

Question

If f(x) = 3x10 - 7x8 + 5x6 - 21x3 + 3x2 - 7, then displaystyle limα → 0(f(1-α)-f (1)/α3+3α) is (A) -(53/3) (B) (53/3) (C) -(55/3) (D) (55/3)

Tardigrade Admin · Accepted Answer

Let f'(x) = 3x10 - 7x8 + 5x6 - 21x3 + 3x2 - 7, f '(x)=30x9-56x7+30x5-63x2+6x f ' (1)=30-56+30-63+ 6 = 66-63-56 = -53 Consider displaystyle limα → 0(f (1-α)-f (1)/α3+3α) = displaystyle limα → 0 (f '(1-α)-(1)-0/3α3+3) (By using Lâhospital rule) (f '(1-0)-(1)/3(0)2+3)=-(f '(1)/3)=(53/3)

Q. If $f (x) = 3 x^{10} - 7 x^{8} + 5 x^{6} - 21 x^{3} + 3 x^{2} - 7,$ then $α \to 0 lim$ $\frac{f ( 1 - α ) - f ( 1 )}{α ^{3} + 3 α}$ is

$- \frac{53}{3}$

$\frac{53}{3}$

$- \frac{55}{3}$

$\frac{55}{3}$

Q. If f(x)=3x10−7x8+5x6−21x3+3x2−7, then α→0lim​α3+3αf(1−α)−f(1)​ is

−353​

353​

−355​

355​

Let f′(x)=3x10−7x8+5x6−21x3+3x2−7, f′(x)=30x9−56x7+30x5−63x2+6x f′(1)=30−56+30−63+6 =66−63−56=−53 Consider α→0lim​α3+3αf(1−α)−f(1)​ =α→0lim​ 3α3+3f′(1−α)−(1)−0​ (By using L’hospital rule) 3(0)2+3f′(1−0)−(1)​=−3f′(1)​=353​

Q. If $f (x) = 3 x^{10} - 7 x^{8} + 5 x^{6} - 21 x^{3} + 3 x^{2} - 7,$ then $α \to 0 lim$ $\frac{f ( 1 - α ) - f ( 1 )}{α ^{3} + 3 α}$ is

$- \frac{53}{3}$

$\frac{53}{3}$

$- \frac{55}{3}$

$\frac{55}{3}$