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Statement 1: If both functions f(t)a n d...

Statement 1: If both functions `f(t)a n dg(t)` are continuous on the closed interval [1,b], differentiable on the open interval (a,b) and `g^(prime)(t)` is not zero on that open interval, then there exists some `c` in `(a , b)` such that `(f^(prime)(c))/(g^(prime)(c))=(f(b)-f(a))/(g(b)-g(a))` Statement 2: If `f(t)a n dg(t)` are continuou and differentiable in [a, b], then there exists some `c` in (a,b) such that `f^(prime)(c)=(f(b)-f(a))/(b-a)a n dg^(prime)(c)(g(b)-g(a))/(b-a)` from Lagranes mean value theorem.

Answer

Step by step text solution for Statement 1: If both functions f(t)a n dg(t) are continuous on the closed interval [1,b], differentiable on the open interval (a,b) and g^(prime)(t) is not zero on that open interval, then there exists some c in (a , b) such that (f^(prime)(c))/(g^(prime)(c))=(f(b)-f(a))/(g(b)-g(a)) Statement 2: If f(t)a n dg(t) are continuou and differentiable in [a, b], then there exists some c in (a,b) such that f^(prime)(c)=(f(b)-f(a))/(b-a)a n dg^(prime)(c)(g(b)-g(a))/(b-a) from Lagranes mean value theorem. by MATHS experts to help you in doubts & scoring excellent marks in Class 12 exams.

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