Find an equation of the tangent line to the curve at the point (1, -1-). y = x³e-x y =

Q: Find the direction in which the maximum rate of change occurs for the function f(x, y) = 5x sin(xy)…

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Q: Given f(10) = 50 and f'(10) = 2 Approximate the following values f(11)~ f(9.5)~ ƒ(10.25)~

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Q: Find and simplify the derivative of f(x) = ln(cosh (ax))

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Q: dy Find by implicit differentiation. dx x²14xy + y² = 14

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Q: 21. A one-sided limit can be used to determine the behaviour of a graph on either side of a 22. A…

A: Completing the given statements

Q: 1. Use the differential form of the chain rule to find if y = ² and u = x² + 1. 2. Find the…

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Q: A stone is thrown straight up from the roof of a 256-ft building. The distance (in feet) of the…

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Q: a) lim x-0 9+x-3 x

A: The solution is shown below-

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

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Q: 31. The surface area of an inflating weather balloon is described by A(x) = 4x² - 1 where x is the…

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Q: Consider the function ƒ(x) = −2x² + 8x – 3. f(x) has a critical point at x = A. Find the value of A:…

A: Application of Derivative

Q: a = (0, 1, 2), 128. c= (1, 0, 1) - b = (-1,

A: Given: a=0,1,2b=-1,0,1c=1,0,-1

Q: Consider the function f(x) Enter an antiderivative of f(x). Do not enter +c as part of your answer.…

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Q: Compute [5t³ - 8t + 1] d dt

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Q: Suppose that a company's sales volume y (in thousands of units) is related to its advertising…

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Q: Evaluate the iterated integral **²y³ dady.

A: K=∫04∫016x2y3dxdywe know ∫xndx=xn+1n+1+c

Q: Consider the function f(x) = 12x5 + 75x¹ – 120x³ +4. f(x) has inflection points at (reading from…

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Q: 1. Find the Cartesian coordinates a. 1 2 I b. -√2₁. 2 3 π

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Q: Find the sum of the convergent series. (Round your answer to four decimal place Σ (sin(7))" n = 1

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Q: For the following exercises, the vectors u and v are given. a. Find the vector projection w= proju v…

A: Given: u=5i+2jv=2i+3j

Q: 8. Below is the graph of f(x) = x³ + x² - 5x+3: a) Find the zeros. b) For each zero-use synthetic…

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Q: Find the point of intersection of the line through (1, -4, 1) and (4, -10, 5), and the plane given…

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Q: The Sixth Gate After walking through the fifth gate, your computer informs you that more than half…

A: Given function f( t ) = 1a( 7t3 - 55t2 + 165 )40

Q: The passcode for this gate is found by determining the domain of the derivative of f(x) and 45 then…

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Q: п Convert the point (p, 0, 0)=(3, 377) 6 expressions, or decimals to at least one decimal place. (x,…

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Q: = 4y cos(2x - 5y) at the point (5,2,8) Find the tangent plane to the equation z =

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Q: Let a = (-3, -5, -2) and 6 = (2, 5, 3). Find a x b. <-5 X, 5 ✔25

A: NOTE: Refresh your page if you can't see any equations. . here we have

Q: For a certain mammal, researchers have determined that the mesiodistal crown length of deciduous…

A: Given: Crown length (in mm) of the molar t weeks after conception L(t)=-.015t2+1.38t-7.1 To find:…

Q: Find the derivate of the functions of at any Use the form f'(c) = lim f(x) - f (c) for a and b X->(…

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Q: Find the maximum of f(x, y, z) = x + y + z subject to the two constraints x² + y² + 2² = 6 and 1x² +…

A: Solution below

Q: A company operates two plants which manufacture the same item and whose total cost functions are…

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Q: After an antibiotic tablet is taken, the concentration of the antibiotic in the bloodstream is…

A: The concentration of the antibiotic in the bloodstream is modeled by the function C(t) = 6(e−0.4t −…

Q: sin 20x sin 21x dx =

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Q: Let f(x) = x4 lnx for all x > 0. I

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Q: 17x³ (In x)² dx =

A: The given integral is: ∫17x3 ln x2 dx

Q: An inverted pyramid is being filled with water at a constant rate of 25 cubic centimeters per…

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Q: Find the points on the cone ² = x² + y² that are closest to the point (5,4,0)

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Q: This was incorrect

A: The given function is; f(x,y)=ln(x3+y3).

Q: - The function ƒ(x) = 2x³ − 33x² + 144x – 2 has two critical numbers. The smaller one is x = and the…

A: Please see the below picture for detailed solution.

Q: z is incorrect

A: We have to find the value of z (Round to 4 decimal)

Q: A ball is dropped from the top of a lighthouse that is 145 feet above sea level. The height…

A: Given height function s( t ) = -16t2 + 145

Q: 6. Evaluate the limit: lim x+-5+ a. 25 b. 2.5 5x X+ 5* C. c. -25 -co d.

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Q: "This passcode consists of the two below limits which include an Remember to type "infinity" for 0,…

A: For x approaching c from the left, x&lt;c  ⇒  x-c5&lt;0The denominator is a negative  approaching…

Q: If x² + y² - 3xy² = -1, find dy/dx in terms of x and y. Using your answer for dy/dx, fill in the…

A: Given equation:- x2+y3-3xy2=-1

Q: How do you find the absolute max and min for problem 45?

A: The given function is: y=x+x2-2x ;          0, 4

Q: The data in the table concerns the lactonization of hydroxyvaleric acid at 25°C. They give the…

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Q: 9. A ladder 25 feet long is leaning against the side of a house. The base of the ladder is pulled…

A: Here -ve sign indicates ladder is decreasing its height along downward at the rate of 7/12 feet/sec…

Q: 2. Find dy/dx and d'y/dx² at the given point without eliminating the parameter : x = 6s², y=-25³ 3…

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Q: P'(W): = P(w) = 6w² - 2w + 4 VW

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Q: The number of different species in Artemis (fictional) is modeled by f(t) = 1000t/((t+3)(t+5)) in…

A: As per question we need to find the extreme points of the function f(t)=1000tt+3t+5, on interval 0≤…