Use the chain rule to help you find dy/dx for each of the following functions: 10. y = (x²+4)³ 12. y = sin(3x+1) 11. y=e³x

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A: As shown in diagram, we can conclude on following step.

Q: 1. Prove the following limits x 4y4 G) lim (x,y) (0,0) (x²+y4)3 = Does not exist

A: Solution is given below:

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Q: 1. The population of a city is growing by the same percent every year. The population at the 2000…

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Q: 5πT 4 Convert the angle from radians to degrees: 5πT 4 O

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Q: d (19) dx [xy] dx

A: We have to find the integral.

Q: In problems 16-19, each limit represents the derivative of some function f at some number a. State f…

A: This question can be solved using the concept of derivative of a function y=f(x) at a given point…

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Q: Solve the system 23x = 92y = 115 -11 X +444 = -55 (x, y) = IS Is there a solution ?

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Q: Find the domains of the following relations. Write them in interval notation. f(x)=√x²-25 (b) x+4…

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Q: a) b) c) -4 -3 -2 -1 lim f (x) x-1 lim f(x) X→-2 lim ¿ x- 2*¹ f (x) ¿ f(x) LO 4+ 3- 2+ 1- 0 H -2+ 1…

A: Given that a graph and we find given limits - a) lim(x tends to 1) f(x). b) lim(x tends to -2) f(x).…

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A: Given :-x=2+t,y=3+12t and Tx2,4=5,Ty2,4=3

Q: Divide as indicated x + 5 5 + 5x +25 6

A: Topic = Algebra

Q: For which interval is the function f(x)=x√√4-x² continuous O (-∞, -4] and [4, ∞) O (-∞, -2] and [2,…

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Q: 13. Recall that nonzero vectors u and are called collinear if there exists a nonzero scalar a such…

A: Given data:- Nonzero vectors are u→ & v→ Nonzero scalar α such that v→=αu→ u→×v→=0→

Q: Make a table of values for the equation. y = x² - 5 X -2 -1 0 1 2 у Sketch a graph of the equation.

A: The given equation y=x2-5 we have to sketch graph of the equation Note:    Multiple questions are…

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Q: onsider the function in the graph to the right. he function has a maximum of at x = The function has…

A: From the given graph

Q: For the function f graphed in the accompanying figure, find the following limits. If a limit does…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 1. Given: F(x) = 3x²+x-4, G(x) = 1 -x and H(x) = e. Find the following. M d. H (0) F (1) h i j F 2x…

A: NOTE: Refresh your page if you can't see any equations. . take x=0 ...................answer(d)

Q: The Z-transform of the following function f[k] = 2.2k + (-5)* - 33 (-4)* is so the constants A and B…

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Q: www Given the function defined by f(x)=3x−1, find f(-

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Q: (a) Find the Taylor series expansion of the function et around x = 0 (b) Use the series above to…

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Q: Use the alternative form of the derivative to find the derivative of the function below at x = c (if…

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Q: 27. A large tank is partially filled with 100 gallons of fluid in which 10 pounds of salt is…

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Q: Solve 273 (Q)dx if Q=0.85x² + 6x + 12 298

A: Given :∫298273QdxQ=0.85x2+6x+12

Q: Compute the surface integral over the given oriented surface: F = y²i + 6j − xk, normal F. ds =…

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Q: d the limit lim X-3 x-2-1 x-3

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Q: 1. Find an equation of the tangent plane to the surface of z = sin(x - 2y) at the point (7,2,0).

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Q: An electromotive force E(1) [120, [0, 0t 20 t> 20 is applied to an LR-series circuit in which the…

A: Let's solve current at time t by using diffrential equation.

Q: Use the divergence theorem to find the outward flux of the vector field F(x, y, z) = 4x²i + 5y²j +…

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Q: 4) - How much work box horizontally 10ft with a force of 2016 applied at an angle of 45° to the…

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Q: Find the average value of the function over the given interval. (Round your answer to four decimal…

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Q: Find the x- and y-intercepts of the graph of the equation. (If an answer does not exist, enter DNE.)…

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Q: 5000 4000 3000 2000 1000 X 50 100 150 200 250 300 350 (b) What is the slope of the graph? 5000 (c)…

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Q: 1. Find the limit if exists or show that the limit does not exist 3x²y² (a) lim (2,3)+(0,0) 24+4 (b)…

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Q: 4. Let w = f(z) = 2iz + 6z, find u and y and the value of fat z = ¹+ 4i

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Q: Find the domain and range of the function. (Enter your answers using interval notation.)…

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Q: lin +²-25 ++-5 2t² + 1lt +5

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Q: lim t→l 1+√t+ √t+√t t² + 1 + 1 t³-2

A: I have solved step by step in detail...and I have written answer up to simplified…

Q: Slopes of Secant and Tangent Lines - Homework 1. For the function f(x) = 5x + 3, find the following.…

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Q: 2. tan o C √उ, oe all

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Q: Determine the set of x-values where y = x - 4 r2 +9r+18 is continuous, using interval notation.

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Q: Consider the function defined as follows: f(x) = 5x² - 8x + 10. f(3+h)-f(3) h as happroaches zero.…

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Q: 6 5 4+- 3 2 1 1 +- I lim 1-8 lim lim → 4¹ 1 0 1 2 y = f(x) →4 T T I T 1 Enter each answer as a whole…

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A: We have to find the value of x that gives greatest capacity.

Q: If f(x) = 7 and g(x) 4x + 3 (fog)(1): (gof)(1) = = √√45x + 4, compute the compositions (fog)(1) and…

A: Given , f(x)= 7 / (4x+3) And g(x)=√(45x+4)