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Evaluate the following limit if it exists:
limx→0 [4x^3]/[tan^(3) x+tanx-x]
limx→0 [4x^3]/[tan^(3) x+tanx-x]
1) if (√5−1)/(√5+1)+(√5+1)/(√5−1)=a+b√5 , find a and b .
2) Simplify : 1/(1+√2−√3) by rationalising the denominator.
2) Simplify : 1/(1+√2−√3) by rationalising the denominator.
Olivia saved $500 in a certificate of Deposit for six months. At the end of the six months she had a return of $50. What is Olivia's rate of return?
1. a. Find the value of a put option with an exercise price of $100 and 3 months to expiration. The stock current price is $100. The 3-month expected price of the stock would be either $80 or $120. The risk-free rate is 3%.
b. What is the value of a call option on the same security with a strike price of $100 and 3 months to expiration?
b. What is the value of a call option on the same security with a strike price of $100 and 3 months to expiration?
Check whether the following functions are continuous or not at x = 0. Also, find
the nature of discontinuity at that point, if it exists.
(i) f(x)= {[(2-x)^(1/2) - (2+x)^(1/2)] / [x] , x≠0 ; 1/√2 , x=0
(ii) f(x)= { x^(2)+1/3, x≤0 ; -[x^(3)+1/3], x>0
the nature of discontinuity at that point, if it exists.
(i) f(x)= {[(2-x)^(1/2) - (2+x)^(1/2)] / [x] , x≠0 ; 1/√2 , x=0
(ii) f(x)= { x^(2)+1/3, x≤0 ; -[x^(3)+1/3], x>0
If a ∈ R is such that o≤a≤ε ∀ ε > 0, then show that a = 0.
The function f defined by = |x-5/2| ,x ∈ R has a local maxima of x=5/2. true/false? justify
A Riemann integrable function is not necessarily differentiable.true/false? justify
Every function differentiable on [a, b] is bounded on [a, b]. true/false ? justify
1/2 is a limit of the interval ]-2.5,1.5[. true/false justify
