Question 5: (1 point) f(x) = + x - 18, find S (1) (a) 215 (b)-875...
4. For this question, define f(x) = (x - 1)e-(0-1). (a) Find f'(x) and f"(x). (b) Find where S is increasing and where / is decreasing (e) Find where S is concave up and where / is concave down. (a) Find all critical points of . For each point you find, explain whether it is a (relative) maximum, a (relative) minimum or neither. (e) Find all points of inflection of f. For each point you find, explain why it is...
(1 point) Given the function f:1-5, 1] + [1,1]; f(x) = cos x, check which one(s) of the properties it has. A. strictly decreasing B. decreasing C. injective D. surjective E. strictly increasing F. increasing G. None of the above
1 point) Consider the Fourier series: nTTc a. Find the Fourier coefficients for the function f(x) 1.2 an b. Use the computer to draw the Fourier series of f(a), for x E[-18, 18], showing clearly all points of convergence. Also, show the graphs with the partial sums of the Fourier series using n5 and n20 terms. What do you observe?
1 point) Consider the Fourier series: nTTc a. Find the Fourier coefficients for the function f(x) 1.2 an b. Use...
1 30% For a paraboloid S: z(x.y)-x2+y, 0sz4 (a) (5%) Find a plane tangent to S at the point P(1, 1, 2) (b) (5%) Find the direction where the derivative of S at P is the steepest (largest) (c) (5%) Find the unit shortest line one S that passes P () (d) (15 %) Determine the flux of F xi+ yj+ zk out of S. s (x, y) y X
1 30% For a paraboloid S: z(x.y)-x2+y, 0sz4 (a) (5%)...
Question 5 4 pts Find the second derivative of the given functions: f(x) = 8x3.9x2 + 6x +4 (a) 48 (b) 48x2 + 18 (c) 48x2-18x (d) 48x - 18 (e) 48x + 18 O (a) O (b) O (c) O (d) O (e)
x²+2x+2 4. Let y=f(x)= x² – 3x-5 (a) Find f(3) (b) Find and simplify f(x) - $(3) X-3 f(x)- $(3) (c) Find lim X-3 (d) Find and simplify $(3+h)-f(3) h 13 (e) Find lim f(3+h) – S (3) h 0 h (t) Find the slope-intercept form of the tangent line to y = f(x) at x = 3. (g) Plot the curve and the tangent line on the same graph, using the form on the window (-3,7]*[-10,10). 5. A car...
f(x+h)-f(x) Find if f(x)=3x2 + 5x-18 h O A. 6x+5-3h 0 B. 6x +5+h 0 C. 6x+5 O D. 6x + 5+ 3h
Final page 5 of 13 4. Let f(x)8+1 a) Find all the critical points. b) Find the interval(s) where f(x) is decreasing. List these intervals c) Find the r coordinates of all relative maxima. d) Find, if they exist, the s-coordinates of all points of inflection e) Determine the intervals where f is concave up. List these intervals
Final page 5 of 13 4. Let f(x)8+1 a) Find all the critical points. b) Find the interval(s) where f(x) is decreasing....
Question 12 of 23 (1 point) Find two functions f and g such that h(x)=(fog)(x) and f(x) * g() + x. n(x) = */7x +5 f(x)=0 and g(x)=0 Question 14 of 23 (1 point) The one-to-one function is given. Write an equation for the inverse function. 2 s(x) = х 3
R(S) Els Gls) Given this system G(s) = K (s² +85+23) (3² +215+18) 33(3+6) (5+13) a. Find system type b. the closed-loop system Find steady-state error of response to B(s) = 6 c. Determine value of K so that the steady stake evvor of system response to R (s) = 1 is 0.2