Question 5: Consider the piecewise function 13x1 if x1 8(1) = 2 If x=1 2x 5...
Suppose that the piecewise function J is defined by f(2)= {**** -1<<3 - 3x2 + 2x + 23, 2> 3 Determine which of the following statements are true. Select the correct answer below: O f() is not continuous at I = 3 because it is not defined at I = 3. Of() is not continuous at 2 = 3 because lim f(x) does not exist. f() is not continuous at I = 3 because lim f() f(3). ->3 f(x) is...
-8 Consider the piecewise function provided below. Find the value of $K$ that makes the function continuous out of f(x) = 2x +1 if x < 2 In(x + k) if x 2 Select one: COS OU b.e-2 Cross out c. es - 2 d. Other Cross out
2. For f(x) = f(x) = $2x+5, Xs1 14 + 3x, x>1 a. Find f (1) b. Find lim f(x) X1 C. Is f(x) continuous? Why, or why not?
ID Let f(x) = /2x=2 | (a) Find f'(x) as a piecewise function (6) Graph y = f'(x) (c) state the domain of f and the domain of f. Find lin tan 4x cos 3x sin 5x X> 12 Find y if y = (3x+5)*(x+4x) (3 Find y' it ya + 10x tanx 7 Let y= (a) Find (6) Find the equation of the tangent line at (74 y' Elf 8 X3 Prove lim (5-) = 4 (a) write the...
Exercise 4 We have the below function: f(x) = { 2x - 1, if x > 2 x +3, if x s 2 a. Find lim f(x) b. Find lim f(x) C. Find f(2) d. Determine if the function is continuous at point 2.
Write neatly please =) 1. Consider the system described by the ODE's X1 = X2 i,--2x,-3x2 +11 Using the State Function of Pontryagin to find the input u that minimizes u2 a. Determine the state function of Pontryagin H b. Find the optimal input and Ho c. Find the matrix A that will yield the governing equations Xy x2 12 If X1 (0) = 1,x2(0)=0 and x1(1)-x-(1)=0 determine the govern equations for λ! (0) and d. (0) in terms of...
2. Sketch the graph of the following functions and find the values of x for which lim f(x) does not exist. b)/(x) = 1, x = 0 f(x)- 5, x=3 c) x2 x>1 2x, x> 3 d) f(x)-v e) (x)- [2x 1- sin x Discuss the continuity of the functions given in problem #2 above. Also, determine (using the limit concept) if the discontinuities of these functions are removable or nonremovable 3. Find the value of the constant k (using...
4. Below is a piecewise function, determine -5 lim,f(x)= c, lim f(x)= e. lim f(x)- d. y = sin x (not drawn to scale) explain Consider the piece of f(x) in the first quadrant resembling e. Determine lim sinand the behavior of the graph near zero. 5. Using your graphing calculator sketch h(x)-x4-2x3 over [-2,2] below, find the critical values and on the graph label the coordinates of any local, global(absolute) minima, maxima or point of inflection on the sketch,...
2. For the function f(x)= (2x² – 3, x>2 19-2x, x<2 find the limits or explain why they do not exist. (a) lim f(x) 1-2+ (b) lim f(x) (e) lim f(x) X2
Answer both and show work. 1y=fle) L-5. Given the graph of the function f(x) shown to the right-the same graph is - used for L-2. Identify any points where f(2) is not con- tinuous and explain why using precise mathematical statements in relation to how the definition of continuity is not sat- isfied. You may refer to work in L-2 rather than repeat it. L-3. Given the function g(2) defined piecewise below, determine each of the following values, showing clearly...