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.
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`underset(xtoa)lim(f(a)g(x)-f(a)-g(a)f(x)+g(a))/(g(x)-f(x))=4` Clearly the LHS is of 0/0 form. `:." "underset(xtoa)lim(f(a)g'(x)-f(a)-g(a)f'(x))/(g'(x)-f'(x))=4" "`(Using L'Hospital's rule) `or" "underset(xtoa)lim(f(a)g'(a)-g(a)f'(a))/(g'(a)-f'(a))=4` or `" "(kg'(a)-kf'(a))/(g'(a)-f'(a))=4` or k=4
LINEAR COMBINATION OF VECTORS, DEPENDENT AND INDEPENDENT VECTORS
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