Home
Class 12
MATHS
Let f(a)=g(a)=k and their nth derivative...

Let `f(a)=g(a)=k` and their `nth` derivatives exist and be not equal for some n.
If `lim_(xtoa) (f(a)g(x)-f(a)-g(a)f(x)+g(a))/(g(x)-f(x))=4` then find the value of k.

Text Solution

AI Generated Solution

To solve the given limit problem step by step, we start with the expression provided in the limit: \[ \lim_{x \to a} \frac{f(a)g(x) - f(a) - g(a)f(x) + g(a)}{g(x) - f(x)} = 4 \] ### Step 1: Substitute \( f(a) \) and \( g(a) \) ...
Promotional Banner

Topper's Solved these Questions

  • LIMITS

    CENGAGE ENGLISH|Exercise Solved Examples|15 Videos

  • LIMITS

    CENGAGE ENGLISH|Exercise EXERCISE 2.1|10 Videos

  • JEE 2019

    CENGAGE ENGLISH|Exercise Chapter 10|9 Videos

  • LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS

    CENGAGE ENGLISH|Exercise DPP 1.2|10 Videos

Similar Questions

Explore conceptually related problems

Let f(a)=g(a)=k and their n t h derivatives exist and are not equal for some ndot If. ("lim")_(xveca)(f(a)g(x)-f(a)-g(a)f(x)+g(a))/(g(x)-f(x))=4 . Find the value of k.

If lim_(xtoa)[f(x)+g(x)]=2 and lim_(xtoa) [f(x)-g(x)]=1, then find the value of lim_(xtoa) f(x)g(x).

If lim_(x->a)(f(x)/(g(x))) exists, then

If f(1) =g(1)=2 , then lim_(xrarr1) (f(1)g(x)-f(x)g(1)-f(1)+g(1))/(f(x)-g(x)) is equal to

f(x)=(x-k)/(5) and g(x)=5x+7 . If f(g(x))=g(f(x)) , what is the value of k?

If f(a)=2 f'(a)=1 g(a)=-1 g'(a)=2 then lim_(xtoa)(g(x)f(a)-g(a)f(x))/(x-a) is

If lim_(xtoa) {(f(x))/(g(x))} exists, then which one of the following correct ?

If ("lim")_(x->a)[f(x)+g(x)]=2a n d ("lim")_(x->a)[f(x)-g(x)]=1, then find the value of ("lim")_(x->a)f(x)g(x)dot

Let f(x)=x^2 and g(x) = 2x + 1 be two real functions. find (f +g)(x) , (f-g)(x) , (fg)(x) , (f/g)(x) .

let f(x) = sqrtx and g(x) =x be function defined over the set of non negative real numbers . find (f+g)(x) , (f-g)(x) , (fg)(x) and (f/g)(x) .