Find the derivative of the function f(x), FIRST using the Product Rule & SECOND Quotient Rule. Ensure both solutions look the same, are simplified and no longer have any negative exponents. f(x) = 6x+5 (2x+1)³

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Q: First make a substitution and then use Answer: integration by parts to evaluate the integral [2 sit…

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Q: For what value of k the following piecewise defined function will be continuous? [k - 2 cos x, e4x+1…

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Q: 6. f(x) = X a. lim f(x) x-0* b. lim f(x) X-0 c. lim f(x) X-0

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Q: dw Use the Chain Rule to find where w = sin 8x cos 2y, x=, and y=t4. dt dw dt (Type an expression…

A: Using to chain rule :

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Q: Solve the following autonomous differential equation with the given initial condition. dy dt =…

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Q: Compute the first partial derivatives of the following function. f(x,y)=4- tan¹ (9x² + 2y²) x=0

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Q: □ 3. Part 3 - Discussion Question Explain the difference between scalar multiplication and matrix…

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Q: Your answer is incorrect. Calculate the integral approximation Se for S₂ 75+1 dx. S6 = .01682

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Q: If a is a nonzero real constant, what is the following limit? x3 a lim xa x a4 Does not exist 1 2a 1…

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Q: 1) (-1)"(4x + 1)″ For what values of x does the series converge? n=0 a) Find the radius and interval…

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Q: What is the rectangular equivalence to the parametric equations? x(θ)=4cosθ+2,y(θ)=2sinθ−5, where…

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Q: Find the equation for (a) the tangent plane and (b) the normal line at the point Po(4,0,4) on the…

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Q: Solve the differential equation with the given initial condition. dy sin x dx y+2' y = with y(0) = 3

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Q: Let f(x, y) x + 4y 2¹+4 I Evaluate f(0, 1)

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Q: g(x) = 4x3 - 4x + ) = (4x³. 18/5 x2 4

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Q: Use the Chain Rule to find dt where z = x cos y, x=t, and y = 6t²

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Q: 5. Find the equation of the tangent to the curve y = ex + x which is perpendicular to the line y =…

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Q: The per capita growth rate of a population of cells varies over the course of a day. Assume that…

A: Given differential equation

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Q: Let R be the region bounded to the right by the graph of x = cos (9y)+6 , to the left by the y-axis,…

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Q: 2. Determine the Cartesian equation of the plane containing these lines: z+2 x-5 z+5 3 and L₂: *5 =…

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Q: 3. True/False. Indicate whether each statement is true (T) or false (F). a) b) The derivative of a…

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Q: Find the linearization L(x,y) of the function at each point. f(x,y) = x² + y² +1 a. (1,1) b. (41)

A: Consider the formula for the linearization for any function linearization for two variables.

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A: Solution:-  given that now using identity

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Q: y= dy xy dxx + 1 with y(0) = 6

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Q: Find the slope of the line tangent to the curve y = 5ª³ at x = 1. 5 15 In 5 5 ln 5 O ln 5

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Q: 1 1. limno 2²+ √1 + t³ dt Note: Do not use L'Hopital's Rule for this problem.

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Q: All change 6. Describe a series of transformations that would transform(x)= x+5 into g(x)=2x-1 Be…

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Q: Use logarithms to solve the equation for t. 20 1 + 5e-0.6t 10

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Q: 6. Determine the equation of the tangent to y = :-xex + ex at x = 0.

A: Explaination of the answer is as follows

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Q: Change the Cartesian integral into an equivalent polar integral. Then evaluate the polar integral. 9…

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A: given triangle lengths 610.02, 1022.5, 538.54