Show by integration that the volume of a sphere of radius r is V=4/3 πr³

Q: The unit price of hamburger of a fast food shop called "MacDonna" increasesd according the formula…

A: Given: "MacDonna" increased the price of a hamburger according to the formula, P=a·bt where, P is…

Q: x – 2 Let g(x) = x + 3 (a) Find the third degree Maclaurin polynomial of g.

A: Solution: So what we need to do to get the desired polynomial is to calculate the derivatives,…

Q: Use the graph of the polynomial function f(x) (a) to solve f(x) = 0, and (b) find the factorization…

A:

Q: Here is a graph of the function f. 4- 3+ 2- -3+ -4+ Use the graph to find the following. If there is…

A:

Q: The graph of the function f is given. y 6 y = f(x) 21 8 (a) By reading values from the given graph…

A:

Q: exercise

A: f(x) = cx4 If x is doubled

Q: d) L{e f, sin dr}

A:

Q: Match each linear equation with its graph РК B Equation Graph Color y = 5x + 4 a. red (R) 2 b. green…

A: Let us consider a line, ax+by=c  Then the intercept form of this line is given by, x/(c/a) + y/(c/b)…

Q: Let A be the area of a circle with radius r. If dr/dt=3, find dA/dt when r=5.

A:

Q: The piecewise function f(x) is graphed below. Use geometric formulas to evaluate the following…

A: From the given graph;

Q: Evaleuate use integration by-lacts.

A: ∫x2e-3xdxUsing integration by parts

Q: Find the point on the line y = 1 – 6 that is closest to the origin. Give your answer in the form (a,…

A: We have to find a point on line which is closest to the origin.

Q: Use the table below to fill in the missing values. f(x) 1 2 8 3 3 4 9. 4 6 7 7 8 6 9 f(5) = || if…

A: We have to find missing values

Q: Determine whether the following equation represents exponential growth or exponential decay.…

A:

Q: Find all vertical and horizontal asymptotes of the graph of the function. (Enter your answers as a…

A:

Q: Calculate the Taylor polynomials T2 and T3 centered at a = 0 for the function f(x) = 11 tan(x). %3D…

A:

Q: ,on what interval(s), if any, is the graph of f(x) incre: always decreasing

A:

Q: For the function f, use composition of functions to show that f 1 is as given. 7x -7 f(x) = =x+1, f…

A:

Q: 29. Prove the following derivatives by using the definition of derivative. (a) (") = n. dx nxn-1

A: topic - derivative and limits

Q: Verify that the function f(x) = x² – 8x + 5 satisfies the three hypotheses of Rolle's Theorem on the…

A:

Q: Find the lengths of the sides of the triangle with the indicated vertices, and determine whether the…

A:

Q: So what is the square units

A: Apologies for the inconvenience. The correct solution is given below: Given function is: fx=ex7 from…

Q: Can

A:

Q: Find dy far y= dx

A:

Q: - 1)*dx

A: ∫02 (x-1)2dx ∫02 x2 -2x +1dx [x3/3 -x2 +x ]02 8/3 - 4+2 -0 8/3 -2 (8-6)/3 2/3

Q: The integrals below give the area of a region in the xy-plane. Sketch the region, label each…

A:

Q: find the derivative of f(x)=x/(x+2) using the limit definition of a derivative

A:

Q: y(x) = tan/3x² + In(5x*))

A:

Q: Evaluate (x + 1)*dx = [(x+1)*dz + f{ (x + 1)*dx

A: Given Problem:- Evaluate ∫13x+12dx

Q: Find the points on the ellipse 25x? + y² = 25 that are farthest away from the point (1, 0). List all…

A: Given equation of ellipse, 25x2+y2=25So, y=±25-25x2 Now distance between the points (x,y) and (1,0)=…

Q: 1) Find the derivatives of the following. Simplify your final answers. d) 1(x) = tanh-1 x + In V1–…

A:

Q: Find the values of constants a, b, and c so that the graph of y = ax° + bx + cx has a local maximum…

A: Given problem:- Find the values of constants a, b, and c so that the graph of y = ax3 + bx2 + cx has…

Q: 2. Given : f(x) = {x² - 3, x+3 6, %3D X = 3

A:

Q: dx Vx2 + 2

A:

Q: Evaluate the integral by interpreting it in terms of areas. (1 — х) dx -5

A: To evaluate the given integral ∫-52(1-x) dx

Q: Find all values of c so that (2, 1, c) and (c – 1, 2, 2c) orthogonal. are

A:

Q: Find the equation of the tangent plane at the point x = xo = 4, y = yo = 1 of the surface %3D z =…

A: Option C is true

Q: 6 Time Taken: Mins Secs The effectiveness of a certain medical injection is modeled by E(t) =…

A: We have to find the time when reading become sufficient and when reading become too low..

Q: 24 How many 3 letter codes can be formed from the word PROJECT if letters cannot be repeated? 7C3 7!…

A: Number of m letter codes from an n letter words without any repetition can be formed in = nPm ways.…

Q: Evdluate the following integral, S Sin3xcosxdx

A: Use the method of substitution and solve the integration.

Q: 5) S V2 + sin 3t · cos 3t dt

A:

Q: Solve for æ: 109z - 2 = 710z – 6

A: To solve for x.

Q: Evaluate x +1)?dx = [{(x+ 1}dx+ f{(x+ 1}°dx %3D

A: ∫13x+12dx=∫12x+12dx+∫23x+12dx⇒563=∫12x+12dx+∫23x+12dx⇒563=193+∫23x+12dx⇒563=193+373

Q: 15 The population of a district is 600 000 at the beginning of 2015. The population P(n) of the…

A: We need to find A,r and % increase.

Q: what are 7 and 8 in standard hyperbola equation? 7) The foci are (-8, 2) and (2, 2). Vertex at (1,…

A:

Q: The function h(t) represents the height of a ball above the ground (measured in feet) in terms of…

A:

Q: Suppose that the functions g and h are defined for all real numbers x as follows. g (x)= 4x+4 h (x)=…

A:

Q: dy Differentiate implicitly to find dx 2x+7xy + 9y + 19y- 8 = 0 + dy %3D dx

A:

Q: dy by implicit differentiation. dx E. Find 1 ー+ー=2 х у 1 x² +y? = xy 2. 1.

A: the process of finding the derivative of a dependent variable in an implicit function by…

Q: 25. Find the constant(s) c for which the function f(x) is continuous on (-∞,+ ∞) (c? — х2 , х<2 12…

A: