Find the arc length for the curve c(t) = (t³ + 1, t² – 3) over the interval 0 ≤ t ≤ 1.

Q: (−1)n n²zn n! Consider the series (-1)” n=1

A: ∑n=1∞(−1)nn23nn!Ratio TestL=limn→∞|an+1an|Where an is the nth term of the series.If L<1, the…

Q: A 100 m long rope hangs from the top of a mine shaft, and is attached to a crate full of coal. The…

A: The objective of this question is to calculate the total amount of work done to lift the rope and…

Q: Considering the interval [−2, 4], does the Mean Value Theorem for integrals hold for f (x) whose…

A:

Q: Hello, I need to evaluate the limits below but the grahp is made on paint, sorry about that.…

A: Given graph of 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: Use the information to find and compare Ay and dy. (Round your answers to four decimal places.) y =…

A:

Q: Find the general solution of the homogenous differential equation 9y" - 30y' + 25y = 0.

A:

Q: 8. Use the method of substitution to evaluate each of the following general antiderivatives 6x² (a)…

A:

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

A:

Q: Suppose that we're making and selling some widget and the revenue (in dollars) when making a widgets…

A: The objective of this question is to find the average revenue, marginal average revenue functions,…

Q: Your company determines that the marginal cost, C', of producing the xth unit is given by the…

A:

Q: 9. Let f(x) = sinx, g(x) = cos x. The functions f and g, considered on the interval 0, π], are…

A: Given that the function are

Q: 224. Suppose that a particle moves along a straight line with velocity defined by v (t) = t² – 3t –…

A: According to our guidelines we are supposed to answer only the first question if you want any…

Q: Use the following function and its graph to answer (a) through (d) below. et f(x) = 6-x, x4. 2 .…

A:

Q: The graph of f(w) = 9 is given below. 10- 8 6 5 4 -4-3 -2 -1 3 1 2 3 4 5 6 7 8 9 Determine the…

A:

Q: 1. For the function g(x) graphed here, find the following limits or explain why they do not exist.…

A: Since the subparts a,b and c of question 1 have been answered i suppose you want the answer for part…

Q: By recognizing each series below as a Taylor series evaluated at a particular value of x, find the…

A: A.1+6+622!+633!+644!+⋯+6nn!+⋯

Q: 3. Use the figure to answer the questions. B M Answer: D C (a) Which pair of corresponding angles do…

A:

Q: Convert the following equation to polar coordinates. x=2y² The polar form of x = 2v² is. (Type an…

A: Given,

Q: Find the average rate of change of the function over the given intervals. f(x) = 12x³ +12; a) [5,7],…

A:

Q: Find the equations of the tangent and normal lines to the graph of the function at the given point.…

A: The equation of the tangent line  to the curve y= f(x) at x= a is  The equation of the normal line…

Q: Perform the following operations and simplify the results. State the domain restriction in each…

A: The domain is the set of all possible input values  for a which function is defined.

Q: Find the indicated term of the binomial expansion. 13 (u³ +21²) ¹³₂ ; tenth term

A:

Q: The curve r(t)= (f(t),g(t)), where f and g are twice differentiable, has f'g'"-f"'g' curvature…

A:

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

A: Given that the function

Q: For the function g(x) graphed here, find the following limits or explain why they do not exist. a.…

A:

Q: 12x 8 °-x X ³/₂ dx 3

A:

Q: a. What is lim g(x)? Choose the correct answer below and, if necessary, fill in the answer box to…

A: As per our company guidelines, we are supposed to answer only the first 3 sub-parts. Kindly repost…

Q: Let h(z) -5+42-42³ 2² Determine the most general indefinite integral of h. I -5+42-423 22 dz P

A:

Q: L³₂x³dx -2 2 1 x+0.5 dx

A:

Q: Find the dimensions of the right circular cylinder of greatest volume that can be inscribed in a…

A: The right circular cylinder is inscribed in a sphere of radius .The aim is to find the greatest…

Q: f(x) = (5z – 3)(4: 6(2-0³) 3-20 f(9) = 3 ၁၂ နှ

A:

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

A:

Q: Let F(x) = sin(6t²) dt. S Find the MacLaurin polynomial of degree 7 for F(x). S Use this polynomial…

A:

Q: Find a formula for the general term an of the sequence assuming the pattern of the first few terms…

A: To find a formula for the general term  of the following sequence.

Q: 1. Use the Limit Comparison Test to determine whether the series below converges or diverges. List…

A:

Q: Find the surface area of the part of the plane z=6+2x+7y that lies inside the cylinder x^2+y^2=16

A:

Q: e Six dx xX (1+lux)

A: We use the method of substitution to evaluate the given integral

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: Consider the functions f(x) = 6 arcsin (6x) g(r)= 12arctan (a) Find the derivatives of f(x) and…

A:

Q: Find the indefinite integral of the function g(x)=e^(2x) sin(3x)dx

A: The objective of this question is to find the indefinite integral of the function g(x) = e^(2x)…

Q: Find T 1 = -1 wwwman x² dx + C

A:

Q: Simplify the following complex fraction; State the domain restriction: 1 X|N 2 1 1 X 1 -

A: To simplify the following complex fraction. To state the domain restriction.

Q: Using the graph of f'(x) find the increasing/decreasing intervals of f, points on  axis which f has…

A:

Q: g. y = ex² +1 h. y = esinx y = ln(sin x) i. j. y = ln² + e√x X 6. L

A:

Q: Eliminate the parameter t to find a Cartesian equation in the form = f(y) for: √x (t) = 4t² y(t) =…

A:

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: Evaluate the following limit lim X→∞0 O O O O I 8 0 10/00 8 −5x² +6x³ + 3x² − x 8x² − 2x³ + 3x - 8

A:

Q: Let sin A = -1/sqrt10 with A in QIII and tanB = 3/4 with B in QI. Answer exactly. Find tan (A+B) and…

A:

Q: Given that f (t) = t² - t - 5 represents the rate at which air is escaping from a balloon in liters…

A: