Proof:
Since |x|<1, we have by binomial theorem, Comparing, the coefficients of y in (1) and (2), we get ..
Since |x|<1, we have by binomial theorem, Comparing, the coefficients of y in (1) and (2), we get ..Theorem:
If x is a rational number, then the sum (e x ) of the exponential series..
If x is a rational number, then the sum (e x ) of the exponential series..Theorem 1:
Let f be continuous on [a, b] and differentiable on the open interval (a, b). Then (a) f is increasing on [a, b] if f '(x) > 0 for each x (a, b) (b) f is decreasing on [a, b] if f '(x) < 0 for each x (a, b) This theorem can be proved by using Mean Value Theorem. We sh..
Let f be continuous on [a, b] and differentiable on the open interval (a, b). Then (a) f is increasing on [a, b] if f '(x) > 0 for each x (a, b) (b) f is decreasing on [a, b] if f '(x) < 0 for each x (a, b) This theorem can be proved by using Mean Value Theorem. We sh..Theorem 7:
Let f be real valued function in [a,b] such that, f is continuous in [a,b]. f is differentiable in (a,b)...
Let f be real valued function in [a,b] such that, f is continuous in [a,b]. f is differentiable in (a,b)...Theorem 4
Let f be a continuous function on an interval I = [a, b]. Then, f has the absolute maximum value and f attains it at least once in I. Also, f has the absolute minimum value and attains it at least once in ..
Exponential Theorem
If a > 0, then prove that..
If a > 0, then prove that..Rolle's Theorem and Mean Value Theorem
Rolle's Theorem: Let f be a real valued function in [a,b] such that f is continuous in [a,b]. f is differentiable in (a,b). ..
Rolle's Theorem: Let f be a real valued function in [a,b] such that f is continuous in [a,b]. f is differentiable in (a,b). ..First Fundamental Theorem of Integral Calculus
If f(x) is a continuous function on the closed interval [a, b], and if Area function is defined ..
If f(x) is a continuous function on the closed interval [a, b], and if Area function is defined ..See what our Users say :
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