Find the derivative of: – 7 sin² ( – 8x³). Hint: sin²(x) = [sin(x)]²...so use the chain rule (twice!).

Q: (c) Let y = (In x)2. Compute y' by using logarithmic differentiation.

A: The given function y=ln x2x We have to find the derivative of y using logarithm differentiation.

Q: Use the formula for nCr to evaluate the expression 4C4.

A: Given: The given expression is:  4C4. n = 4 r = 4 Formula Used: Crn = n!r!(n-r)!

Q: The function s(t) describes the motion of a particle along a line. s(t) = t3 − 7t2 + 6t   (a) Find…

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Q: The variable interest rate on a student loan changes eachJuly 1 based on the bank prime loan rate.…

A: Given for the years 1992–2007, The rate can be approximated by the model r(x)=−0.115x2+1.183x+5.623…

Q: Please have a systematic way of solution (Question-Solution-Final Answer-Conclusion format) E.…

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Q: -6 (-3,1) -5 86°F Sunny I 1 -4/ -3 -2 1 / -1 4 3 2 - 0 -1 -2 -3 -4 -5 -6 2 W Use the graph to…

A: Given query is to find the slope of the tangent line.

Q: 1. If an ((¹+√5) - (¹-√5)n), find a, and a₂.

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Q: Find the interval of convergence of the following series Σ(-1)₂(x - 2)n n5n n=1

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Q: Find the following limit. lim x-x 2+ x - 4x³-4 5 x³x²+1 Number

A: ans=  -4/5

Q: me of a Cube The volume V of a cube with sides of length x in. is changing with respect to time. At…

A: Volume of cube is side cube

Q: You are dealt one card from a standard 52-card deck. Find the probability of being dealt a heart.

A: Given: Total number of cards = 52 Formula used: Probability = Number of favourableNumber of outcome

Q: Use the formula for nCr to evaluate the expression 10C6.

A: The expression is given by, C610 n=10r=6

Q: Enter your answer as an ordered pair. Provide your answer below: f(x) = 7x² - 12x - 8

A: The given function is  f(x)=x2-12x-8

Q: 7x - 4 3 – – 4x 4x² dx

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Q: 15. Evaluate each expression using the given table of values: -2 -1 1 f(x) 1 0 -2 1 2 g(x) -1 b.…

A: To use the table of values for finding the values of given function.

Q: Set up the integral to be used to find the volume V, using both methods from Chapter 7, of the solid…

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Q: graph each function.f1x2 = 1 x

A: Given, fx=1x

Q: Construct a polynomial function with the stated properties. Reduce all fractions to lowest terms.…

A: degree of polynomial=2zeros x=-2 and x=7

Q: 10. Determine the convergence of the following series using the root test. If the root test is…

A: Given data:- The given equation, ∑n=1∞n+1n+2n

Q: Find the numbers at which g is not continuous. Justify using the definition of continuity. x+2 if x…

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Q: lim asin x→0 | cr x

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Q: Find the directional derivative of f(x, y) = direction of Q(2, −2). NOTE: Enter the exact answer.…

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Q: Evaluate the following integral using trigonometric substitution. x² 441-x² S dx

A: ∫x2441-x2dx

Q: 11 Find the derivative of f(x) = -15sinx + +3√√x-5. X

A: Given function:- fx=-15sinx+11x4+3x7-5

Q: If f(x) = sin x, find ƒ'(x) 5 5 sin(x) cos(x) Find f'(2)

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Q: I need to find the integral of [math]\frac{\cos(2x)}{\cos^3x}[/math]

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Q: Consider the ellipsoid x² + y² + 4z² = 41. The implicit form of the tangent plane to this ellipsoid…

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with…

Q: x=t+3 and y=²+2t Part: 0/2 Part 1 of 2 (a) Eliminate the parameter and write an equation in…

A: The parametric equations are x = t+3                         .........1y = t2+2t…

Q: Rewrite the following quadratic function in vertex form. Provide your answer below: f(x)=0 f(x) =…

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Q: ow the steps below for the given function. (Do not use mixed numbers in your answers.) 8x + 5y: we…

A: Given query is to find the derivative by indicated methods.

Q: Compute the directional derivative of the following function at the given point P in the direction…

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Q: 2y X in the direction of (1, 2). Then, Suppose f(x, y) (a) ▼ f(x, y) = (b) ▼ ƒ(6, π) = = = sin (c)…

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Q: Evaluate S9 cos √2x dx using a substitution followed by integration by parts.

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Q: 2. y=x+c₁e* + C₂е¯x

A: Given :y=x+c1ex+c2e-x

Q: Consider the function f(x) = 3x²-5x+2. Use it to find f(4), f(-1), and f(a + 3). f(4) = 30 O…

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Q: 1. Solve for Txyz given the function T(x, y, z) = z tan (In x - √y)

A: We need to find partial derivative. NOTE - As per Bartleby guidelines we can solve one question.…

Q: Graphing the Cube Root Function(a) Determine whether f1x2 = 23 x is even, odd, or neither. State…

A: Given function is cube root function i.e., f(x)=x3

Q: A car has 12,500 miles on its odometer. Say the car is driven anaverage of 40 miles per day. Choose…

A: Given data:- A car has 12500 miles on its odometer Car is driven an average of 40 miles per day N is…

Q: f(x)=(2x+1)^4   Find the values of x where the tangent line is horizontal Values of X= ___

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Q: 4. Consider Line L with defining equation 2 y - ²x + 1/ . = 6 A. Find two ordered pairs (x₁, y₁) and…

A: see below the answer and calculation

Q: (a) Using a graphing utility, graph f1x2 = x3 - 9x for- 4 ... x ... 4.(b) Find the x-intercepts of…

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and…

Q: 7. 1 (x) == x¹- -2x³ + x-10. Find the hypercritical value(s) of f(x)=

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Q: True or False: The following function is continuous on R. True O False f(x) = if x sin x 44

A: Given function:- fx=sinxif x<π4cosxif x≥π4

Q: Find the area of the shaded region. f(x) = x² - 4x³ + 12x². g(x) = - 3x +90 The area is (Type an…

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Q: N 10 9 8 7 6 5 3 2 1 2 Based on the graph above, estimate to one decimal place the average rate of…

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Q: Evaluate lim 1 1 x 2 X-2 X-2 direct substitution. 1 1 X 2 O lim X-2 X-2 1 1 X 2 O lim X-2 X-2 O lim…

A: The objective of the question is evaluate the limit and choose the correct option.

Q: For the piecewise linear function f(x) graphed below, find the following. (If an answer does not…

A: Given: To find: limx→2- fx , limx→2+ fx, limx→2 fx

Q: Please have a systematic way of solution (Question-Solution-Final Answer-Conclusion format) E.…

A: Solution

Q: Authorities conducted an investigation and found that the chemical Trioxin was illegally dumped into…

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Q: Find the area of the region bounded by the curves y = x² 3 x - 3x and y= 3 x 1 - 3x on the interval…

A: Let's find area of region bounded by two curves.