1.Given the function f(x)=1/x, using 3 rectangles of equal width, find an approximation to the area...

1.Given the function f(x)=1/x, using 3 rectangles of equal width, find an approximation to the area between the curve and the x-axis over the interval [4,8] if the heights of the rectangles are found by evaluating the function at the left endpoints, right endpoints, and midpoints of each subinterval created by a partition of the interval given.

2. Given the function, f(x)=−x3+6x2 using 6 rectangles of equal width, find an approximation to the area between the curve and the x-axis over the interval [2,6] if the heights of the rectangles are found by evaluating the function at the left endpoints, right endpoints, and midpoints of each subinterval created by a partition of the interval given

Expert Solution

milcah answered 2 years ago

Approximate the area under the graph of f(x) and above the x-axis with rectangles, using the...

Approximate the area under the graph of f(x) and above the x-axis with rectangles, using the following methods with n=4. f(x)=88x+55 from x=44 to x=66 a. Use left endpoints. b. Use right endpoints. c. Average the answers in parts a and b. d. Use midpoints.

Find f(x) if f is a linear function that has given properties. f(-1)=1, f(3)=9 f(x)=

1. You are given the function f(x) = 3x^4 + 4x^3 a) Find the x and...

1. You are given the function f(x) = 3x^4 + 4x^3 a) Find the x and y- intercepts. b) Find the critical number(s) of f. c) Find the interval(s) of increase and decrease of f. d) Find the relative maximum and minimum value(s) of f. e) Find the hypercritical number(s) of f. f) Find the interval(s) of upward and downward concavity of f. g) Find the point(s) of inflection of f. h) Sketch the graph of f. 2. You are...

Estimate the area under the graph of f(x)=1/(x+4) over the interval [-1,2] using five approximating rectangles...

Estimate the area under the graph of f(x)=1/(x+4) over the interval [-1,2] using five approximating rectangles and right endpoints. Rn= Repeat the approximation using left endpoints. Ln=

area between curves 1. Find the area between x=1 and x=3 for: f(x) = x+4 and...

area between curves 1. Find the area between x=1 and x=3 for: f(x) = x+4 and g(x)=1 2. Find the area between x =-1 and x=1 for: f(x) = 2-x^2 and g(x) =3 3. find the area between: f(x) = x^2 and g(x) = 2x+3 4. find the area between: f(x) = 4-x^2 and g(x) =3x

Let f(x) = x^3 − x on [−1, 1]. Find the true area of the shaded...

Let f(x) = x^3 − x on [−1, 1]. Find the true area of the shaded region using a limit of Riemann sums, taking the sample points to be the left endpoints. Hint: to ease the computations, you can use the fact that (a + b)^ 3 = a ^3 + 3a^2 b + 3ab^2 + b^3 (which follows by expanding the cube). Verify your work by evaluating the corresponding definite integral using the FTC.

Find the linear approximation of the function f(x,y)= e^(x^2 + 4xy - 2y^2) at (1,2) using the aproximate f(0.99,2.01)

-- Find the linear approximation of the function f(x,y)= e^(x^2 + 4xy - 2y^2) at (1,2) using the aproximate f(0.99,2.01) -- find Zvu for z= f(x,y), x=uv , y= v^2 + u^2 -

1. Which of the following is the linear approximation of the function f ( x )...

1. Which of the following is the linear approximation of the function f ( x ) = 2e^sin (7x) at x = 0? Group of answer choices y=cos⁡(7)x+2 y=7x+2 y=14x+2 y=2x+7 y=e^7x+14 2. Recall that Rolle's Theorem begins, ``If f ( x ) is continuous on an interval [ a , b ] and differentiable on (a , b) and ___________, then there exists a number c …'' Find all values x = c that satisfy the conclusion of Rolle's...

1, Using rectangles whose height is given by the value of the function at the midpoint...

1, Using rectangles whose height is given by the value of the function at the midpoint of the rectangle's base, estimate the area under the graph using the first two and then four rectangles. f(x)= x3 between x=2 and x=4 A, using two rectangles to estimate, the area under f(x) is approximately = ---------? B) using four rectangles to estimate, the area under f(x) is approximately= ----------? 2, Using rectangles whose height is given by the value of the function...

Question1: Find the interval of increase and decrease of given function f(x)=3x^5-5x^3 f(x)=1/3 x^3-9x+2

Question