Question

In: Math

the figure shows the graph of f(x) = ex. in the exercise 1 to 4, use...

the figure shows the graph of f(x) = e^x. in the exercise 1 to 4, use transformation of this graph to graph each function. be sure to give equation of this the asymptotes. use the graph to determine each function's domain and range. if applicable, use a graphing utility to confirm your graph

1). g(x) = e^x-1

2). g(x) = e^x+2

3) h(x) = e^-x

4) g(x) = 2e^x

Expert Solution

The graph for y=e^x is :

Thus the final graph for y=e^x-1 with its asymptote is as follows :

2.

The final graph for y=e^x+2 with its asymptotes is as follows :

3.

The graph for y=e^-x with its asymptotes is as follows :

4.

The graph for y=2e^x with its asymptotes is as follows :

milcah answered 2 years ago

(a) Consider the function f(x)=(ex −1)/x. Use l’Hˆopital’s rule to show that lim f(x) = 1...

(a) Consider the function f(x)=(ex −1)/x. Use l’Hˆopital’s rule to show that lim f(x) = 1 when x approaches 0 (b) Check this result empirically by writing a program to compute f(x) for x = 10−k, k = 1,...,15. Do your results agree with theoretical expectations? Explain why. (c) Perform the experiment in part b again, this time using the mathematically equivalent formulation, f(x)=(ex −1)/log(ex), evaluated as indicated, with no simplification. If this works any better, can you explain why?...

The graph of f(x) =2x + 1 is given below. a. Use 4 approximating rectangles with...

The graph of f(x) =2x + 1 is given below. a. Use 4 approximating rectangles with right hand endpoints to approximate the area under f(x) between x = 0 and x = 2. b. Use a definite integral to find the exact area over the interval [0. 2].

The graph here shows transformations of the graph of f(x) = 2x. What is the equation for the transformation?

The graph of f(x) = sin(2x)/x is shown in Figure 20. Is the function f(x) continuous at x = 0? Why or why not?

Use finite approximation to estimate the area under the graph f(x)= 8x2 and above graph f(x)...

Use finite approximation to estimate the area under the graph f(x)= 8x2 and above graph f(x) = 0 from X0 = 0 to Xn = 16 using i) lower sum with two rectangles of equal width ii) lower sum with four rectangles of equal width iii) upper sum with two rectangles of equal width iv) upper sum with four rectangle of equal width

1: Given that f(4) = 6 and f'(x) = 2/x2+9 for all x. a) Use a...

1: Given that f(4) = 6 and f'(x) = 2/x2+9 for all x. a) Use a linear approximation or differentials to estimate f(4.04) b) Is your estimate in part (a) too large or too small? Explain. 2: a) Given f(x) = (x + 3)sinx, find f'(π) using logarithmic differentiation. b) Find the value of h'(0) if h(x)+xsin(h(x))= x2+4x-π/2

10. For what values of x in the interval [1, 4] does the graph of f(x)=−x^3+6x^2...

10. For what values of x in the interval [1, 4] does the graph of f(x)=−x^3+6x^2 −9x−1 satisfy Rolle’s Theorem? Include a sketch and a brief explanation of what’s going on in this problem. 11. Evaluate each limit. Provide a brief explanation of how you can apply the “top heavy, bottom heavy, it’s a tie” strategy. lim x→∞ 1 / (2x+sinx) 12) Draw a diagram and solve: What is the exact area of the biggest isosceles triangle you can inscribe ...

For the following exercises, use the information about the graph of a polynomial function to determine the function. Assume the ...The y-intercept is (0, 1). There is no x-intercept. Degree is 4. End behavior: as x → −∞, f(x) → ∞, as x → ∞, f(x) → ∞.

The y-intercept is (0, 1). There is no x-intercept. Degree is 4. End behavior: as x → −∞, f(x) → ∞, as x → ∞, f(x) → ∞.

(a) Estimate the area under the graph of f(x) = 4 cos(x) from x = 0...

(a) Estimate the area under the graph of f(x) = 4 cos(x) from x = 0 to x = π/2 using four approximating rectangles and right endpoints. (Round your answers to four decimal places.) R4 = Sketch the graph and the rectangles. WebAssign Plot WebAssign Plot WebAssign Plot WebAssign Plot Is your estimate an underestimate or an overestimate? underestimate overestimate (b) Repeat part (a) using left endpoints. L4 = Sketch the graph and the rectangles. WebAssign Plot WebAssign Plot WebAssign...

Let f(x) = 1 + x − x2 +ex-1. (a) Find the second Taylor polynomial T2(x)...

Let f(x) = 1 + x − x2 +ex-1. (a) Find the second Taylor polynomial T2(x) for f(x) based at b = 1. b) Find (and justify) an error bound for |f(x) − T2(x)| on the interval [0.9, 1.1]. The f(x) - T2(x) is absolute value. Please answer both questions cause it will be hard to post them separately.