1. The graphs of f and g are given below. Use the graphs to answer the...
1. (9 points) Referring to the graphs given below, use properties of limits to find each limit. If a limit does not exist then state that it does not exist. y = f(x) y = 8(%) R -1 - 1 -2 lim f(x) - lim g(x)- 10 10 lim x-0 g(x) lim f(x) - lim g(x)= lim (f(x) + g(x)]- lim f(x) - lim g(x) - 8(x) lim x- f(x)
Use the graphs of f(x) and g(x) shown below to find lim f(g(x + 1)) x1 y = f(x) y=g(x) A 2 2 А B 3 Does not exist
(1 point) The figures below show the graphs of the exponential functions f(x) and g(x), and the linear function, h(x). The function f(x) has y-intercept 0.75 and goes through the point (1,6). The function g(x) has y-intercept 6 and goes through the point (2,6/49). The function h(x) has y-intercept 5 and goes through the point (a, a + 5). y = f(x) y = g(x) y = h(x) (Click on a graph to enlarge it.) help (formulas) (a) Find a...
9. Explain why the function below is discontinuous at the given number a.Sketch the graph of the function 1 if x #-2 f(x)= х+2 a =-2 if 1 х%3D—2 9. Explain why the function below is discontinuous at the given number a.Sketch the graph of the function 1 if x #-2 f(x)= х+2 a =-2 if 1 х%3D—2
The graphs of f and g are given. Use them to evaluate each limit, if it exists. (If an answer does not exist, enter DNE.) (a) \(\lim _{x \rightarrow 2}[f(x)+g(x)]\)(b) \(\lim _{x \rightarrow 1}[f(x)+g(x)]\)(c) \(\lim _{x \rightarrow 0}[f(x) g(x)]\)(d) \(\lim _{x \rightarrow-1} \frac{f(x)}{g(x)}\)(e) \(\lim _{x \rightarrow 2}\left[x^{3} f(x)\right]\)(f) \(\lim _{x \rightarrow 1} \sqrt{3+f(x)}\)
Given the function ry g(x, y) = g(x, y) lim (x,y)(0,0) a. Evaluate iii. Along the line y i. Along the x-axis: x: iv. Along y x2: ii. Along the y-axis: g(x, y) exist? If yes, find the limit. If no, explain why not. b. Does lim (r,y)(0,0) c. Is g continuous at (0,0)? Why or why not? d. The graphs below show the surface and contour plots of g (graphed using WolframAlpha). Explain how the graphs explain your answers...
Referring to the graphs given below, use properties of limits to find each limit. If a limit does not exist then state that it does not exist. y = f(x) y = g(x) lim f(x)= lim g(x) = f(x) x- lim x+0 g(x) lim lim g(x) = lim [f(x)+g(x)] = x-1 lim f(x) = lim g(x) = lim --+ f(x) h- h derivative of f(x) = 2x² + 3x is f'(x) = 4x +3. The steps are what count here!...
A contour map for a function z=f(x, y) is given: Answer the following questions: Question 1. A contour map for a function z S(z,y) is given: -2 k-1 k-1- k-2 Answer the following questions. (a) (1 point) What is f(-1,1)? (b) (2 points) Describe the set of all points (r, y) such that f(z,y) = 0. Which of the following graphs best represents the graph of this function? (c) (1 point) B. A. D. Question 1. A contour map for...
Problem 1. [12 points; 4, 4, 4- Consider the function f(x,y) 1 2- (y-1)2 (i) Draw the level curve through the point P(1, 2). Find the gradient of f at the point P and draw the gradient vector on the level curve (ii) Draw the graph of f showing the level curve in (i) on the graph (iii) Explain why the function f admits a global minimum over the rectangle 0 x 2, y 1. Determine the minimum value and...
(1 point) Use the two graphs below to answer the following questions. (a) The graph of is the graph of scaled horizontally choose the scaling factor 1)by compression by a factor of 5 2) by compression by a factor of 4 3) by compression by a factor of 3 4) by compression by a factor of 2 5) no horizontal scaling 6) by expansion by a factor of 2 7) by expansion by a factor of 3 8) by expansion...