Hello please help solve this calculus problem attached down below.

Q: Find the principal P that must be invested at rate r, compounded monthly, so that $500,000 will be…

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Q: c) y" +10y' + 25y = 0

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: Verify that the hypotheses of the Mean-Value Theorem are satisfied for ƒ(x) = √√x + 16 on the…

A: To verify that the hypotheses of the Mean-Value Theorem are satisfiedfor  on the interval , and to…

Q: A farmer has 2000 ft of fencing and plans to construct a rectangular pen. Find the dimensions of the…

A: Given data: The total length of fencing is 2000 ft.

Q: Determine whether Σ(-1)^-1 is convergent. 1 √n +3 n=1 rk in order to roccio full in utiol onadit

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Q: Find the angle 8 between the vectors in radians and in degrees. u = cos · cos(™)i + sin(π)j, v =…

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Q: Use the given information to find the left- and right- hand Riemann sums for the following function.…

A: given function

Q: Let f(x) = x^4 − 4x^3 − 20 (a) Find the zeros of f"(x). Then decide which of these are inflection…

A: According to our guidelines we are supposed to answer only the first three subparts of the question.…

Q: The surface whose equation in cylindrical coordinates is r = 5 is... a cylinder a cone half of a…

A: The given equation of is

Q: Find the equation of the tangent line to y = (x³ + 2x + 3) eª at the point where x=0. The equation…

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Q: Find the value of k that makes the antidifferentation formula true 1 - dx 3+ 7x k Inl3+ 7xl +C

A: To find the value of  that makes the antidifferentiation formula true.

Q: Trust Fund A deposit of $20,000 is made in a trust fund that pays 5% interest, compounded…

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Q: part b) why do you divide theta by 360?

A: Formula for area of sector of a circle is given by               Where

Q: Using the graph of 5 + cos(7x), for 0 ≤ x ≤ 3³7, list the following quantities in increasing order:…

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Q: Use Newtons Method to find the third approximation -x3, for the root of f(x)= x^3-x^2-1=0 Hint is…

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Q: Find a vector-valued The ellipsoid r(u, v) = function whose graph is the indicated surface. x2 1/2²…

A: To find a vector-valued function whose graph is the indicated surface. The ellipsoid

Q: A candy box is made from a piece of cardboard that measures 37 by 20 inches. Squares of equal size…

A: Given:A candy box is made from a piece of cardboard that measures 37 by 20 inches. Squares of equal…

Q: In the following exercise, given that 1 1-x = ∞ Σa x" for x < 1, n=0 use term-by-term…

A: Power series.

Q: Solve the rational equation below, please upload a picture of your work. 14 2²2-22

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Q: n's Theorem to evaluate the line integral (y - x) dx + (2x - y) dy C wen path. : boundary of the…

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Q: The graph of the derivative f'(x) is given below. On what interval(s) is the function f(x) concave…

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Q: 5. Determine the volume of the solid obtained by rotating the region bounded by z = ³ - 5y² and the…

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Q: Let y = 3e¹ 2x³+e-4z. . Which is y'? You will need to simplify to find the answer.

A: The given function is

Q: For y = xe^(-1/x), find the intervals of increase and decrease.

A: given function To find: the intervals of increase and decrease.

Q: f(x)= [5x+3] e-2x

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Q: #2.) S sec secx tanx sinx (secx) dx

A: we need to find out the integration.

Q: At a certain instant in time, the number of cars, N, traveling on a portion of a certain highway can…

A: The objective of the question is to find the estimated number of cars, N, traveling on a 1-mile…

Q: n 17 years, Anthony Beechwood is to receive $100,000 under the terms of a trust established by his…

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Q: Use the reference angle to find the exact value of the following expression. sin 585°. (Simplify the…

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Q: Evaluate by interpreting as the area of a geometric figure (draw the figure and use geometric…

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Q: Exercise 4. Prove the following claims. (i) Let f: R² →→ R be defined as f(x, y) := { 3 xy x² + y²…

A: The condition of function in R2 must fullfill in order to be continuous isf(a, b) = lim (x, y) -&gt;…

Q: 7-year period from 2004 to 2011. D 5

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Q: In an opinion poll, 715 or 63% of people interviewed were opposed to the issue asked.  How many…

A: Given In an opinion poll, 715 or 63% of people interviewed were opposed to the issue asked.Let…

Q: Find the Maclaurin series for the given function. 14e x What is the Maclaurin series of f(x) =…

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Q: Find the derivative of the given function. f(x) = e6 sin(x) 6 sin(x) cos(x) f'(x)= 6e What is the…

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Q: II. Differentials Recall, the DERIVATIVE values represent SLOPE values on a given function. Slope =…

A: A derivative of a function is a representation of the rate of change of one variable in relation to…

Q: Use the initial condition y(2) = 7 to determine the value of A that will satisfy the initial value…

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Q: 6) Show that=1

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Q: Find u x v, v x u, and v x v. u = (-6, 2, -7) v = (-2,-5, -3) (a) ux v (b) vxu (c) vxv

A: given vectors

Q: Let G be a function whose derivative is shown below. Assume the domains of G and G'are 0 ≤ x ≤ 12. 8…

A: We have given a graph of G'(x) in the interval . We have to find the value of G( 6) and coordinates…

Q: 17. The velocity graph of a braking car is shown. Use it to estimate the distance traveled by the…

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Q: Find the dimensions of the rectangle of largest area that has its base on the x-axis ans its other…

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Q: True or False: If a ‡ b and if ſå |ƒ(x)|dx = 0, then f(x) = 0. True O False

A: The given statement is If  and if  then

Q: 2. Determine the value of the discriminant for the quadratic equation y = 1.4x² - 6x +5 and use that…

A: we are given the quadratic equation and we need to find its discriminant.

Q: Verify that the hypotheses of Rolle's Theorem are satisfied for f(x) = cos(x) on the interval [3π 5π…

A: 1) f(x) is continuous on [a,b],2) f(x) is differentiable on (a,b), and3) f(a) = f(b)then there…

Q: Find the general Solution of :- - dy dx = 3 Sin 2x Cos 2X

A: The given differential equation is

Q: (a) Sketch the graph of r = 8 cos 0 by plotting at least 4 points in polar coordinates. Label the…

A: given a equation

Q: Question 4.21) Evaluate the following limits. sin² (1)-1 1-4 A) lim 2/2+1 B) lim x-0 Question 4.22)…

A: a) limx-infinity x[arc(tanx)-pi/2]According to Bartleby guidelines we solve only one question repost…

Q: A particle moves along the x-axis in such a way that its acceleration at time t for t≥ 0 is given by…

A: Accelearation of the particle is given by

Q: Find the work done with a spigot 1m above a trough that measures 9m long and has sides that are…

A: