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[ 10 pts.] 9. Use the alternative limit definition of derivative to determine whether the function...
Determine if the following piecewise defined function is differentiable at x = 0. x20 f(x) = 4x-2, x2 + 4x-2, x<0 What is the right-hand derivative of the given function? f(0+h)-f(0) lim (Type an integer or a simplified fraction. I h h+0+
[4 Pts. Use the definition of continuity to show that the function f is continuous at <=0 10 g(x)= 3-4
find the limit f(x) = 2x2 -3, if x-2 13-x, ifx < -2 then, determine if the function is continuous at x=-2
The directional derivative of the function f(x, y) = 2x In(y) in the direction v =< 0,1 > at the point (1,1) is equal to 2. Select one: O True False
5. 6 pt Determine whether the function f(x) is continuous and/or differentiable at x = 1. (x2+1 f(x) = { 12, >1 1 <1
10. Use the limit definition of the derivative to calculate the derivatives of the following functions. a. f(x) = 2x2 – 3x + 4 b. g(x) = = x2 +1 1 x2 +1 c. h(x) = 3x - 2 a. 11. Find the derivative with respect to x. x² - 4x f(x)= b. y = sec v c. 5x2 – 2xy + 7y2 = 0 1+cos x 1-cosx cos(Inu) e. S(x) = du 1+1 + + f. y =sin(x+y) g....
5. Use the limit definition to find the derivative of f(x) = V3x + 2. (6 points) 6. Find the derivatives of the following functions. Do not simplify after taking the derivative. 5 points each a. f(x) = (4x2 +1) c. h(x) = arcsin(3x2+ 2x-1) b. h(x) = 3sec(x2)
Determine if the limit exists, Graphically
b.) lim X1 x2 + 3 2 x<> 1 x=1
Use the limit definition of partial derivatives to compute the partial derivative of the function f(x,y) = 2 - 2x + 5y - 3x?y at a point (3.4). a. Find f (3.4). b. Find f (3.4). f|(3.4)=0 (Simplify your answer.) 13(3.4)=0 (Simplify your answer.)
+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)?...