Find the average rate of change of the function over the given intervals. f(x) = 12x³ +12; a) [5,7], b) [-6,6] a) The average rate of change of the function f(x) = 12x³ + 12 over the interval [5,7] is (Simplify your answer.)

Q: A circle has an initial radius of 50 ft when the radius begins decreasing at the rate of 5 ​ft/min.…

A: A circle has an initial radius of 50 ftThe radius begins decreasing at the rate of 5 ​ft/min

Q: 17. Suppose you want to fence three sides of rectangular region where one side is bordered by a…

A:

Q: 1 The equation z = 1 3 3 x² + y² is given in Cartesian coordinates. Convert the equation to…

A:

Q: et P(x, y) denote the point where the terminal side of angle 8 (in standard position) meets the unit…

A: The figure

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A:

Q: 2. S x³ +1 x³ - x² da dx

A:

Q: The formula for the braking distance of a car is: 0.03361 v² μl d= where: . d is the braking…

A: given that,and find the d value for the given velocities?

Q: 4. n=1 ne-n

A: Since you have asked multiple questions in a single request so we will be answering only first…

Q: Find two positive numbers whose product is 100 such that the sum of the first and four times the…

A: Find two positive numbers whose product is 100 such that the sum of the first and four times the…

Q: The Taylor series for f(x) = x³ at-4 is cn(x + 4)". Find the first few coefficients. Co= C1 = C2 -…

A:

Q: Specify the period and amplitude for the function. period amplitude -20 -15 -10 -5 11111111 y…

A:

Q: 2. Prove that (₁ + ²)" is convergent by using the Monotone Convergence Theorem.

A:

Q: find the limit if it exists, or show that it does not exist.  lim (x,y)→(0,0) (x^4 −y^4)/x^2+y^2

A:

Q: se the given information to evaluate each expression. (Enter your answers in exact form.) sin a =…

A:

Q: lim У-у-г уг -30+2 зу Уже

A: We have to findlimx→−2

Q: 4-Z 4-z-2y k √ ₁² √²-²² ² -² -²y xyz²dx dy dz = 1 2 0 0 0

A: To solve for unknown.

Q: f(x) = ln(x)

A: A Taylor series is given by f(x)=∑k=0∞f(k)(a)k!(x−a)k

Q: cos(x) - 1 lim 10 esin(z)-1-x

A:

Q: The approximate rate of change in the number of design patent applications received in recent years…

A:

Q: Use the parametric equations of an ellipse,x=6cos(θ),  y=3sin(θ),  0≤θ≤2π,to find the area that it…

A: The objective of the question is to find the area enclosed by the ellipse defined by the parametric…

Q: (c) A= 58°, a = 9, b = 5 (d) A = 90°, b= 6, c = 8

A: (c) Given that,    By using sine rule,

Q: 8. Find the linearization L(x) of f(x)=√√x² +9 at x = -4.

A: Given that the function

Q: 5. 6% a. x-2 dx 1-sin 2x 2 x-sin-x dx 2 + tan² x x + tan x - dx

A:

Q: Tonic 2: Functions The function f(x) = log10 (x-2) + 1 is given. a) Describe the transformations…

A: According to bartleby guidelines we are supposed to do only first three subparts . If you want more…

Q: Find the following limits: lim (x² – 13) a. X--3 b. lim 8(t-5) (t - 7) t-6 2x+5 lim x-211-x³ c. C.

A: To find the following limits.

Q: 2 T If f sin (3 x) sin (n x) dx = π, then n = 0 Number

A:

Q: Determine whether the series converges or diverges. Σ 5 sin (²) n n = 1

A: The given series is

Q: Find T5 (2): Taylor polynomial of degree 5 of the function f(x) = cos(x) at a = 0. T5(x) = Using the…

A: We have to find the Taylor polynomial of cosx of degree 5. Then using the Taylor Remainder Theorem,…

Q: Find the derivative of h (x) = csc¹ (x) Oh' (x) = -4 csc¹ (x) cot(x) ○ h' (x) = 4 csc¹ (x) cot² (x)…

A:

Q: Using the Rules for Finding the Derivative of a Function. For the following exercise, assume that…

A:

Q: Given the graph of f (x) below, what is the open interval(s) ov which f'(x) is positive? 3 N -8 -7…

A:

Q: 800 The demand function for a widget is given by p= 90+ where p is the price of the widget in…

A: The given demand function is,

Q: Find the complete solution of the linear system, or show that it is inconsistent.

A: A system of equations is inconsistent when it has no solution.that is no real numbers as variable…

Q: At which of the value(s) of x below does f(x) = ²³² +5x² + 25x + 1 have a horizontal tangent line? O…

A: Given that, the function is .We need to find the value of x for which the given function has a…

Q: If the marginal revenue for ski gloves is R'(x) = -0.5x + 55 and R(0) = 0, find the revenue…

A:

Q: Suppose parametric equations for the line segment between (4, 2) and (4, - 2) have the form: [ x(t)…

A: The line segment between the points (4, 2) and (4, -2) has parametric equations,It is also given…

Q: Use the parametric equations of an ellipse, x = a cos(8), y = b sin(0), 0 ≤ 0 ≤ 2π, to find the area…

A: Given that the parametric equation

Q: Find the integral of the following function by parts So 0 sec²0 de Ja where a = 6.08, b = 7.05 in…

A: The given integral is

Q: d) Plot the x and Vintercepts on the Cartesian Plane. Label the axes and title the graph. Clearly…

A: The volume of the box

Q: f(x) = -2(sin(3x + pi/2)) + 1 for x is an element of [0, 4pi/3] State the phase shift, period,…

A: The given function is  , The standard equation of Amplitude Phase shiftVertical shiftTime period

Q: how much is 2*2

A: The question is asking for the product of 2 and 2.

Q: Let f(x) [0, 2π). = To enter , type Pi (with a capital P) sin x. Determine the x-value(s) where the…

A: The given function .The aim is to find the value of  in the interval  for which the function has…

Q: A hemispherical tank with a radius of 8 m is filled from an inflow pipe at a rate of 4 m^3/min ​(see…

A: The hemispherical tank of radius

Q: Find the slope of the tangent line to the graph of the polar equation at the point specified by the…

A: Given that the polar curve

Q: Set up and evaluate the triple integral needed to compute the volume of the solid bounded above and…

A:

Q: 1) Write a complex number in a standard form z = x + ly:: 2+i (2- i)(3i+ 4)(i+1)

A: The given complex number is

Q: 5 1 - 9x Compute the first few coefficients of this power series: Represent the function -Co C1 C₂…

A: The given function is 5/(1-9x).

Q: lim x-0+ x lim x-0-x² g. h. 2 1+x i. lim (¹+2) ² →? x-2

A: Note:-Since you asked multiple sub parts questions, according to our policy we can solve only first…

Q: Use the surface integral in Stokes' Theorem to calculate the flux of the curl of the field F = 4zi +…

A: We have to find the flux of the curl of the field F using surface integral in Stoke's Theorem.Given…

Q: Let g(t) = - 503 t Determine the most general indefinite integral of g. - 5 + dt

A: Given,