Find indicated quantity if it exists.
How to solve it? Let F =< -2, x, y2 >. Find S Ss curlF.nds, where S is the paraboloid z = x2 + y?, OSz54.
Let f(x)= kx + 5 x-1 for x<2 for x > 2 . Find the value of k for which f(x) is continuous at x=2.
Determine if the limit exists, Graphically b.) lim X1 x2 + 3 2 x<> 1 x=1
If 4 - x2 = f(x) < 4+x2 for –3 <x<3, find lim (2) 20
8. Let f:D → R and let c be an accumulation point of D. Suppose that lim - cf(x) > 1. Prove that there exists a deleted neighborhood U of c such that f(x) > 1 for all 3 € Un D.
Let X be an exponential random variable such that P(X < 27) = P(X > 27). Calculate E[X|X > 23].
Exercise 1. Let f : R R be differentiable on la, b, where a, b R and a < b, and let f be continuous on [a, b]. Show that for every e> 0 there exists a 6 > 0 such that the inequality f(x)- f(c) T-C holds for all c, x E [a, 히 satisfying 0 < |c-x| < δ
4- Find f'(x) if f(x) is the given expressions. i) f (x ) = zsin ">" + ln cosh - 4x ii) f(x) = tanh-- 4x etanh4x
1. Let X be a random variable with pdf f(x )-, 0 < x < 2- a) Find the cdf F(x) b) Find the mean ofX.v c) Find the variance of X. d) Find F (1.75) e) Find PG < x < +' f) Find P(X> 1). g) Find the 40th percentile.*
Use the Mean Value Theorem to demonstrate that In(1 + x) < x, given that x > 0.