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Theorem: Let f(x)→L, g(x)→L' then x→a and cεR  then we have (a) f(x)+g(x)→L+L' (b) cf(x)→cL (c) f(x)g(x)→LL' as x→a (d) if further L'≠0 then g(x)≠0 f…

Evaluate the  limits: SOLUTION  : by substituting the limit directly we are going to obtain zero(0) which shows that the limit does not exist.

In probability theory , Chebyshev's inequality guarantees that, for a wide class of probability distributions , "nearly all" values are close to the mean —…

Bernoulli Trials: the Bernoulli trial states that if there are two independent trials with two outcomes. Either True or False , Yes or No , Success or Failure , and …

Bhāskara II also known as Bhāskarāchārya or "Bhāskara the teacher" is an Indian mathematician and astronomer. his works represent a significant contribution t…

Examine whether The Mean Value Theorem(M.V.T) is applicable to the following functions for the interval in which they are defined.    SOLUTION: the f…

Theorem: The Mean Value Theorem States that let a real valued function f be continous on a closed interval [a,b] and differentiable in the open interval (a,b) then th…

Examine whether Rolles Theorem is applicable to the following functions for the interval in which they are defined . SOLUTION  Below is a table of intervals of funct…

In calculus, Rolle's theorem essentially states that any real-valued differentiable function that attains equal values at two distinct points must have a stationary …

Determine which of the following are differentiable at 0.                                   (i)                                 f(x)=x|x| (ii)  (iii)  SOLUTION  (i) the…

QUESTION   Show that f is differentiable at 1 and find f'(1) SOLUTION:  we first check the differentiability of f(x)=2x-3 at (0,1), to do this we use the test of di…

Theorem: If f(x)→L as x→a and f(x)→L' as x→a then L=L' Proof: to proof the theorem we first proof for f(x)→L as x→a, which is |f(x) - L|<∂ whenever n≥N₁ the…

Below we are going to discuss about some of Nigeria’s great mathematicians whose efforts and contributions in mathematics are widely acknowledged in the western world…