4. Show that lim -oxsin(1/2) = 0 by by appealing directly to the definition of limit....
[4 Pts. Use the definition of continuity to show that the function f is continuous at <=0 10 g(x)= 3-4
(h) Define f : [0, 2] + R by 122 if 0 <<<1 f(x) = { ifl<152 Using the limit definition of the derivative and the sequence definition of the limit prove that f'(1) does not exist.
+1 4. Consider the function ISO 0<<1 -1 = 1 0 1<*52 (x - 2)2 => 2 (a) (10) Use the definition of the limit of a function at a point to evaluate with proof (b) (10) Use the definition of continuity at a point to prove that /(x) is not continuous at -1. (e) (2) Is /(x) uniformly continuous on (-1,2)? If it is, prove it. Other- wise, explain why not. (d) (8) Is f() uniformly continuous on (1,3)?...
[ 10 pts.] 9. Use the alternative limit definition of derivative to determine whether the function 8sinh(x/2) ifx<2 f(x)= is differentiable or not differentiable at 2x²+x-1 if x2 x=c=2 Show all work !!!
send help for these 4 questions, please show steps
Definition: The AREA A of the region S that lies under the graph of the continuous function f is the limit of the sum of the areas of approximating rectangles A = lim R, = lim [f(x)Ax +f(x2)Ax+...+f(x)Ax] - 00 Consider the function f(x) = x, 13x < 16. Using the above definition, determine which of the following expressions represents the area under the graph off as a limit. A. lim...
1. (2 points) Using the definition, find the Laplace Transform of the function: e21, 0<t<3 f(t) = 3<t
Prove the statement using the ε, δ definition of a limit.
Prove the statement using the ε, definition of a limit. lim x → 1 6 + 4x 5 = 2 Given a > 0, we need ---Select--- such that if 0 < 1x – 1< 8, then 6 + 4x 5 2. ---Select--- But 6 + 4x 5 21 < E 4x - 4 5 <E |x – 1< E = [X – 1] < ---Select--- So if we...
Determine if the limit exists, Graphically
b.) lim X1 x2 + 3 2 x<> 1 x=1
(Hint: think of tan as a fraction!) lim (1 - .) tan 7. Suppose a function f(x) satisfies f'(x) < 0 and f(x) > 0 for all x 20. > 0 for all x > 0. Consider the function F(x) := ["s(t) dt whose domain is 0,00). Is F(x) an increasing or decreasing function
be a continuous random variable with probability density function 3. Let for 0 r 1 a, for 2 < < 4 0, elsew here 2 7 fx(x) = (a) Find a to make fx(x) an acceptable probability density function. (b) Determine the (cumulative) distribution function F(x) and draw its graph.