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

Question

If f(x) = 3x10 - 7x8 + 5x6 -21x3 + 3x2-7, then displaystyle limα→0 (f(1- α) - f(1)/α3 + 3 α) 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)-0/3α2 +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​3α2+3f′(1−α)(−1)−0​ (By using L’hospital rule) =3(0)2+3f′(1−0)(−1)​=3−f′(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

$- \frac{53}{3}$

$\frac{53}{3}$

$- \frac{55}{3}$

$\frac{55}{3}$