Evaluate the following limits Copyright-protected assessment question. Do not distribute. 4 + 6x x →∞ 4 - 6x² a) lim Copyright-protected assessment question. Do not distribute. 83 8x³8x² 3x 10x 8x³ Copyright-protected assessment question. Do not distribute. b) lim x →∞ 10 c) lim x →→ ∞ - 9x² - 8x + 8 11x + 4

Q: Find the linear approximation of f(x) = ln x at x = 1 and use it to estimate In(1.04).

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: By considering different paths of approach, show that the function below has no limit as…

A: Here, the given function is: f(x,y)=x4x4+y2 1) Now, to find along with which set of curves is f a…

Q: 2n 3n+ 1 (a) Determine whether {an}_1 is convergent. Problem 2. Let an = (b) Determine whether an is…

A: The given sequence is: an=2n3n+1

Q: SS. Y = sin²³√₁-α³² o^u² 1 1-Uª differentiate

A:

Q: 3. S (6x² + √x − ³) dx

A:

Q: In the figure below, set-up the integral expression when the area bound by the functions y = 1, y =…

A: The given region is bounded by the functions:y=1x,   y=x   and   x=4

Q: 26 85 k=1 087 (k+5)!

A:

Q: or the integral ffe dydz, ez² etch the region of integration and evaluate the integral. ur sketch…

A: For the integral ∫02∫0xex2dy dx  Sketch the region and evaluate the integral.

Q: Find the domain of the function. (Enter your answer using interval notation.) f(x) = log5 (82x)

A: doamin of logx  is  x>0f(x)=log5(8-2x)for domain  8-2x>0

Q: Which would be the four non-zero terms of these series?

A:

Q: 3 to 4-x² dx

A:

Q: Determine the particular solution yp of the given ODE y(4)−5y′′+4y=10e−3x A. yp=12e−3x B. yp=4e−3x…

A: Let's find perticular solution of given diffential equation.

Q: Evaluate the double integral zy³ + z²ydA R where R = {(x,y) | 1 ≤ x ≤ 2, 1 ≤ y ≤ 3} Z 300 200 100 0…

A:

Q: 1. f is increasing on the intervals 2. f is decreasing on the intervals 3. The relative maxima off…

A:

Q: Determine the domain that results from eliminating the parameter in the set of parametric equations…

A: Given     xt=6t+3    ⇒ t=x-36        ............................i and  yt=7t+3 y=7x-36+3

Q: Write the sum using sigma notation: 4 + 6 + 8 + 10 + ... + 28 A = B = A ΣΒ, where n=1

A:

Q: Find the Taylor polynomial T3(x) for the function f centered at the number a. -4x f(x) = e sin(5x),…

A:

Q: x = 7v2u+7w, y = 2u - 9v - 3w, and z = 7v5u - 10w implies (x, y, z) d(u, v, w) =

A:

Q: Use implicit differentiation to find y² + 6x³ = 7y - 4x² dy dx > Next Question dy dx

A:

Q: {21} s² +4 9-1 3 (28+5)³ 2} ₁-55

A:

Q: Consider the following integral. +5 4 dx Given the substitution u = x64, find du. du = 6x5 X Rewrite…

A: The answer is given below:

Q: Show that the function r(0) = sec 0 - +5 has exactly one zero in the interval 0, 83 r'(0) = Can the…

A:

Q: A trough filled with a liquid that weighs 300 lb/ft³ is 10 ft long and its cross-section is in the…

A:

Q: Find the value or values of c that satisfy the equation f(x)=x+ C= 1 x' 19 19 f(b)-f(a) b-a =(Use a…

A: We will use the concept of differentiation and mean value theorem to solve the value for c

Q: Consider rotating "R" about the x-axis to form a solid of revolution. When we integrate to find the…

A: We have to given integral function to find volume generate by revolution of solid. Topic :-…

Q: (b) Use a convergence test of your choice to determine whether the following series converge or…

A: Please see the below picture for detailed solution.

Q: If there is more than one solution, use a comma to separate your answers. Express your answer(s) in…

A:

Q: 10. Consider the function f(x) = 8x8 + 8x² − 5x³ An antiderivative of f(x) is F(x) = Ax" + Bx" + Cx²…

A: f(x)= 8x8+8x7-5x3-10

Q: Which of the following is the correct form of the particular solution yp of the given ODE…

A:

Q: Find the value or values of c that satisfy the equation [1³] C= f(x) = 4x + f(b)-f(a) b-a (Use a…

A:

Q: By treating as an improper integral, evaluate namely by considering the limit and using l'Hôpital's…

A:

Q: Find the inverse laplace of F (s) = consider a²b², ab 0 Of(t) Of(t) Of(t) 1 (s²+a²) (s²+6²) Of(t) =…

A:

Q: Let x be the number of stereos sold with installation and y be the number sold without installation.…

A:

Q: ← 1 5+2x -=-(- ₁ -/-) ₁ Let f(x)= a. Use the following definition of the slope of the tangent line…

A:

Q: A graphing calculator is recommended. Find the Taylor polynomial T₂(x) for the function f centered…

A:

Q: 3.1 A farmer grows a certain type of a tree in a greenhouse and usually sells the tree after 4 years…

A: The height of the tree if given by the differential equation: dhdt=3.5t+15 ;      h(0)=14

Q: xp 6

A:

Q: 2.3 Evaluate the following integrals x+2 dx √x²+4x ₁x(x-1)³ dx a. b. SJ

A: The given integral can be evaluated by using the substitution method.

Q: Estimate I = J (a) Left endpoints. x sin(x) dx using the partition {0, co | == -} and 6' 43' 2

A:

Q: 4. [x - yarctan()]dx + xarctan()dy = 0

A:

Q: A lighthouse is 7 miles off a straight shoreline. Fourteen miles down the coast is a restaurant…

A: According to question,Distance Between lighthouse and shoreline = 7 mi

Q: 1 7 dx x ln(3x)

A:

Q: Write the parametric equations below as a Cartesian equation by eliminating the parameter. x(0) = -5…

A: We need to convert the given parametric equation into Cartesian equation

Q: Given f''(x) = 2x - 6 and f'(-2) Find f'(x) and find f(4) = = 4 and f(− 2) = 1.

A:

Q: 2. f(cosxsecxcotx)dx

A: To evaluate the integral by using substitution method

Q: Find the area on the first quadrant (QI) and under the curve given by x = y² + 1from its…

A:

Q: Verify that the function satisfies the three hypotheses of Rolle's Theorem on the given interval.…

A:

Q: Determine the area of the region bounded by y = Hint: Intersections occur above the x-axis O 36 + In…

A:

Q: 27. Determine whether the function f(x) = −2x² + 5x has a maximum or minimum at 5 the point where x…

A: Given function;- fx=-2x2+5x

Q: At exactly two of the labeled points in the figure below, which shows a function f, the derivative…

A: The figure given is