1. Compute the first, second, and third derivative of a. f(x) = x² In(x+ 1)

Q: a. y'=-20x (3– 5x')" 32. Suppose that x and y are both differentiable functions of t and are related…

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Q: Find the minimum of f(x,y) = 7x + 3y on the ellipsoid 7x2 + 4y2 = 8. Leave your answer correct to…

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Q: The percentage P of doctors who accept a new medicine is given by P(t)=100(1-e^-0.30t) where t= time…

A: Answer is in step 2.

Q: For each of the following series, use the sequence of partial sums to determine whether the series…

A: For the following series, by using the sequence of partial sums to determine whether the series…

Q: a) Find the value of a such that the series 00 a E(-1)" is equal to . If it is not possible 2" n=0…

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Q: Graph the function f(z) = – 2x´ and draw the tangent lines to the graph at points whose…

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Q: Use Green's theorem to evaluate the line integral along the given positively oriented curve. | 8y dx…

A: Green's Theorem:- To find the line integral of a function along a closed curve C…

Q: Given the power series Σ 4 (x - 3)" - n = 0 n + 2n Find the "Radius of Convergence" for the series.

A: Radius of convergence of the given power series  ∑n=0∞ 4n2+2nx-3n

Q: Justify your answer whether the following functions are continuous or not at a certain point or…

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

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Q: write the function as a piecewise function. f(x) = ⌊3 − 4x⌋

A: Find your answer below

Q: If the average value of a function f(x) is 3 on the interval [0,1] then the average value of f(x)?…

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Q: 1. (-1)*z* (2k)! for |피 < ® COS I = for |피 < 0 Use the power series representations for cos r and e-…

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Q: The functions y1 = ex and y2 = e-3x solutions for the homogeneous DE: are both y" – 9y = 0. Then,…

A: y''-9y'=0Since y1=e3x  , y2=e-3x are the solutions of homogeneous DE  Then complementary function is…

Q: Section 1.5 In Exercises 1 and 2, we refer to a function f, but we do not provide its formula.…

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Q: Use the chain rule to find the derivative of f(z) = 4/10z5 + 4x4 Type your answer without fractional…

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Q: A college student borrowed $44,000 to pay for tuition, room, and board. Some of the money was…

A: A college student borrowed $44,000 to pay for tuition, room , and board. Some of the money was…

Q: Find the y sec! (+) %3D

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Q: Evaluate the integral. (Use C for the constant of integration.) 2 dx ex/2

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Q: 15. Suppose you start at the point (0, 0, 3) and move 5 units along the curve x = 3 sin t, y = 4t, z…

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Q: Find a power series for f(x) = In(1+ x). Hint: In(1+ x) is one antiderivative of (whose 1+x power…

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Q: dy +cosh 2y=0 dx 3. sin x ans: sinh 2y-2cosx3Dc

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Q: 2. Use the Mean Value Theorem to show that f(x) = 2x sinh(x – 1) + 2* - x has a critical number…

A: Let's find.

Q: Find the average value of the function LX TEX f (x) =4sin| on the interval [3,6]. COS 4

A: Dear learner, as per our guidelines we can provide the solution for first one only. Kindly post…

Q: Evaluate the following limit. (3x²-y") lim (x.y)→(4,-4)

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Q: V * 00 > Find the critical points of the following function. Use the Second Derivative Test to…

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Q: d 4) (1+ x)* = (Logarithmic differentiation) dx

A: We have to find the differentiation.

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: Given the following limits, lim f(x) = 4, lim g(x) = 9, lim h(x) = 6, %3D %3D x→6 x→6 use the limit…

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Q: Solve the equation In(x + 2) = cos - 3) + 2.5 using the Newton-Raphson method with an initial value…

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Q: Find two unit vectors orthogonal to a = (2, 5, 0) and b = (3,0, 5) Enter your answer so that the…

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Q: 33 1 2s5 6s3

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Q: We can find the inverse of a matrix by row reduction. Suppose matrix A is given and we wish to find…

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Q: Calculate the derivative: d dx * ST (6t3 – 9t) dt = -

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Q: Find the exact length of the curve. x = 8 + 12t2 y = 3 + 8t3 Osts 3

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Q: x2 - 6 Calculate the derivative function of g(x) Write your result as a single fraction. 2x + 1 =…

A: Given: g(x)=x2-62x+1

Q: MY NUTES A projectile is shot upward from the surface of Earth with an initial velocity of 110…

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Q: Consider the solid obtained by rotating the region bounded by the given curves about the y-axis. y =…

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Q: dx 6. S e2x+1

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Q: Find the Taylor series for f(x) centered at the given value of a and the interval on which the…

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Q: If f'(x) and g'(x) exist and f'(x) > g'(x) for all real x, then the graph of y f(x) and the graph of…

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Q: Find the AREA of the region enclosed by r =2+2 sin 0. A. 27 В. 4т С. 6т D. 8T

A: Here we have to find the area of the region enclosed by r = 2+2 sin(theta) .

Q: Given the power series 00 Σ (x - 2)" n = 0 n Find the "Interval of Convergence" for the series. A…

A: Ratio Test : Consider a positive term series ∑ an  and                  L = limn→∞ an+1an , then (i)…

Q: Find Ax) if A1) =-5, and the tangent line at x has slope (3x- 1)e*-2*.

A: The tangent line at x has slope 3x-1e3x2-2x and f1=-e2

Q: Evaluate the following limit. (8x² -) lim (ху) - (6, -5) Select the correct choice below and, if…

A: In this question, we will find the limit of the function along two different paths .

Q: 9 п+7 00 is divergent. n=1 1+7 n Select one: True False

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Q: Let A(x) = So f(t) dt, with f(x) as in figure. 1.0 0.5 A(x) has a local minimum on (0, 6) at x =…

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Q: Let f be the function graphed below. If 30 subintervals of equal length are used, write a summation…

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Q: Find a power series representation for f(x) = x2 1+ x3 ° By differentiating the power series…

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Q: For eac. ation, determine whether it shows a direct variation (that is, shows directly proportional…

A: Let's find.