Let f(x)=3 x10-7 x8+5 x6-21 x3+3 x2-7. Then find the value of displaystyle lim h arrow 0 (f(1-h)-f(1)/h3+3 h).

Question

Let f(x)=3 x10-7 x8+5 x6-21 x3+3 x2-7. Then find the value of displaystyle lim h arrow 0 (f(1-h)-f(1)/h3+3 h). (A)  (B)  (C)  (D)

Tardigrade Admin · Accepted Answer

L Hospital rule: given limit is f'(1)(-(1/3))=(53/3) f'(x)=30 x9-56 x7+30 x5-63 x2+6 x f'(1)=-53 So, -( f '(1)/3)=(53/3)

Q. Let $f (x) = 3 x^{10} - 7 x^{8} + 5 x^{6} - 21 x^{3} + 3 x^{2} - 7$ . Then find the value of $h \to 0 lim \frac{f ( 1 - h ) - f ( 1 )}{h ^{3} + 3 h}$ .