Use the quotient rule to find the derivative of 4x² + 2 k(x) 6x - 2 =

Q: lim X→18 V 1 + 16x6 5-x³ +3

A: We know that the value 1/infinity=0

Q: Find the limits as x→ ∞o and as x → -∞ f(x) = 4x³ - x4 lim f(x) = X-8 lim f(x) X→18 =

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Q: Can someone help me with this please?

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Q: Evaluate the definite integral. 8 0 1 4 3 3x + 13 X + 9 dx

A: Explanation and some important formulas::-

Q: 3 a) The function f(x) = 5x² + 8x-13 has an inverse. function g g' (-13) = д g'(o) Find g'l 10 (-13)…

A: Given function fx=5x3+8x-13

Q: A function f is shown in the graph at right. The domain of the function is all real numbers except x…

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Q: Find the area under the curve y = 8x4 over the interval [0, 4]

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Q: 4. Nahla is renting a vehicle for a business trip. a) Nahla calculated the rate of change in rental…

A: Slope is a measure of the steepness of a line .

Q: 32 Determine the maximum and minimum values of the function f(x) = 2x+² on the interval -2≤x≤8.

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Q: Find y SX a) y = 3 sin (x² + 5x - 3) y' = c) y = sin" (6x) y'= b) xE5X+2 d) y = In (2x) Y₁ = Y y' =

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Q: 39. [x+y=8 √x - y = 4 40. x + 2y = 5 x + y = 3

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Q: Suppose that a cup of soup cooled from 90°C to 40°C after 15 minutes in a room whose temperature was…

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Q: The rate of depreciation (in dollars per year) for a certain truck is given by the function below,…

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Q: he limit. (If the limit is infinite, ent (√49 lim t →∞ 49t² + 8 - 7t)

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Q: 12. Consider the equation x = ( 1 ) x x' -5 -3 Express the general solution in terms of real valued…

A: The given system of differential equation is:x'=1-51-3 x

Q: Let s(t) = 6t³ +81t² + 360t be the equation of motion for a particle. Find a function for the…

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Q: Tell the maximum number of zeros that the polynomial function may have. Then use Descartes' Rule of…

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Q: 2-x Find the domain of f(x) = x2+18x-40

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Q: Use the algorithm for curve sketching to sketch the following:( Show all steps) a) Y=x²-3x+6 x-1

A: a)y=x2-3x+6x-1

Q: A company finds that the rate at which the quantity of a product that consumers demand changes with…

A: The given rate at which the quantity of a product is given by D'p=-10000p2, where p is the price per…

Q: Use Descartes' Rule of Signs to determine the number of positive real zeros of the following…

A: By using Descartes' Rule of Signs to determine the number of positive real  zeros of the following…

Q: A colony of bacteria is grown under ideal conditions in a laboratory so that the population…

A: To find out the number of bacteria present initially.

Q: v(t) = 5 sin(t) — 4cos(t); _s(0)=0

A: We know that the velocity formula v(t)=ds/dt

Q: Given f(x) = e with f"(0) = 8, f'(0) = 2, ƒ(x) = || + C. then f(x) Note that your answer should not…

A: Given the question :- F"'(x)=ex with f"(0)=8,f'(0)=2

Q: d²y and find the slope and concavity (if possible) at the given value of the parameter. (If an…

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Q: 5. Use the graph on the right. At what rate does the airplane descend into the airport? Answer to…

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Q: Suppose a product's revenue function is given by R(q) = −8q² + 200q. Find an expression for the…

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Q: 7. The width of a rectangle is decreasing at a rate of 1 cm/s and the length is increasing at a rate…

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Q: You are driving a car away from home. Your velocity (miles per hour) t hours after noon is given by…

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Q: For the given function, determine the following if possible. If it is not possible, explain why. You…

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Q: Consider the following. f(x) = x2/3, Xo = 1 (a) Find the linear approximation L(x) to fat xo. L(x) =…

A: The linearization or Linear approximation of a function f(x) at the point x0 is given by…

Q: 21. f x² In(1+x) dx

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Q: QUESTION 5 Describe the level curve f(x,y)= In[y (x4-5x3-lnx+1)]=9

A: By the answering guidelines of Bartleby, We can answer only first question from multiple question,…

Q: Find a linear function h, given h(7)=-16 and h(-4)=17. Then find h(8).

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Q: 8 If f is continuous and f²f (t) f(t) dt = 10, find the following integral. [²1² f(t³). dt = ||

A: We have to evaluate the integral. For this we will use substitution method to convert the integral…

Q: Question 5 If y = (sin x)", then dy (a) g[ln(sinx) +cot] (e) none of these (b) y[ln(sin x) + cot x]…

A: Given: y=(sinx)x We have to find dy/dx

Q: a) The Metal Can Company has an order to make cylindrical cans with a volume of 250 cm³. What should…

A: Let us take the dimensions of a cylinder with the height h and the radius of the base r, we also…

Q: Find the total area of the region between the x-axis and the graph of y=-x²-3x, -6≤x≤2.

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Q: For the following polynomial function f(x) = 3xº + 2x² + 6x − 8, find the lower bound within which…

A: f(x)=3x6+2x3+6x-8

Q: Consider the following. y = 3x² - In(x), (1, 3) (a) Find an equation of the tangent line to the…

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Q: what is the final answer?

A: We need to show steps to find maximum velocity.

Q: b b [ 2² dx = 4 ve [dz = 3 dx α a

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Q: A particle moves with a velocity of v(t) ft/s along an s-axis. Find the displacement and the…

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Q: 18 • Σ =1

A: let  G=∑k=118(k2)

Q: Solve the following initial value problem. d²s dt² (St-). -7), s'(0) = 200, s(0) = 0 = -25sin 5t- S=…

A: To solve the following initial value problem. d2sdt2=-25 sin5t-π2, s'0=200,  s0=0

Q: d²y Find d and and find the slope and concavity (if possible) at the given value of the parameter.…

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Q: if y=2u^4-4(u^2-2u)^2 and u=√x-1 find dy/dx when x=10

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Q: Find exactly the vector oppositely directed to v = (3) and half the length of v. < Dell IH

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Q: Suppose f(4) = -1 and f'(4) = -10. An object moves along the curve y³ - 2x² f(x) - 2x = 51. For a…

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Q: Find the first three non-zero terms of the Maclaurin Series expansion for the function, f(=)…

A: For ln(1 - 6x), we have: f(x) = ln(1 - 6x) f'(x) = -6/(1 - 6x) f''(x) = 36/(1 - 6x)^2 f'''(x) =…