Question-1: Prove that 1-cos(x) lim 0 Hint: Use the conjugate of 1- cos(x). 20 is zero using that lim_0 sin(x) T - 1

Q: 6. Simplify the following equation y = 2√√x × 4²√√x. A. y = 8x²¹/8 = 6x²/5 + x-3 B. y = 8x³/4 C. y =…

A: To differentiate given equation.

Q: Verify that f and g are inverse functions. 11. f(x) = x + 6, g(x)= x - 6

A: As per our guidelines we can answer only 1 question so kindly repost the remaining questions…

Q: The current ratio (assets/liabilities) of company X is 3.4. Given that the current assets are…

A: Solution: current liabilities = current assetsX

Q: 10. Use the graphs below to answer the following questions. Give your answer in interval notation.…

A: From the given graph we have to find the solutions of the inequality 2x+4<-x+1 and 2x+4≥-x+1.

Q: Let r₁(t) = (-7, -3, −2) + t(0, −1, −1) and r₂(s) = (-1,1,5) + s(2, 0, 1). Find the point of…

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Q: Estimate the area between the x-axis and the graph of f(x) = 9 - x² over the interval [−2, 1] by…

A: The given curve is f(x)=9-x2 The graph given is

Q: • Solve using homogenous equation v² dx + x(x + v)dv = 0 a.)xv² = c(x + 2v) b.)xv = c(x + 2v) c.)xv²…

A: We can solve the given homogeneous differential equation by using the substitution v = ux.

Q: Consider the following. (If an answer does not exist, enter DNE.) f(x) = 2x³-12x2² +2 (a) Find the…

A: Explanation of the answer is as follows

Q: I have f(x) = integral x to x^4 (t^4) dt. It asks for f'(x). Please help

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Q: Biologists have noticed that the chirping of crickets of a certain species is related to…

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: Find all zeros of f(x) = x³ + 5x² + x + 5. Enter the zeros separated by commas.

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Q: Find the angle between the diagonal of a cube of side length 20 and the diagonal of one of its…

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Q: Practice Problem 2. For x > 0, consider the function Compute the indefinite integral X F(x) = [² / /…

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Q: A real estate investment, originally worth $7000, grows continuously at the rate of 400e0.05t…

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Q: O O O k|m9 3πT 05/2 Na -TT O T FTT/2 5 4 3 2 1- b Given the graph of the function ƒ (x) = \tan(2x)…

A: We are required to find the graph of the function f(x)=13tan(2x)

Q: Make a rough sketch of the graph of the function. Do not use a calculator. Just use the graphs given…

A: Given: y=3x+2 Graph to be used: (given)

Q: 4. If f'(x) = 12x² + 6x −4, f(0) = 4 and f(1) = 1, find f(x) Ans f(x) = x² + x³ - 2x²-3x+4

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Q: The kinetic energy E of a rocket of mass m, traveling at velocity v is given by the formula E =…

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Q: PART THREE: ab* + k ➤ In this part, you are going to explore the effect of parameter k to the…

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Q: 4. Write the equation of a line containing the point (5, 150) with slope m = slope-intercept form. 1…

A: We can solve this as follows:

Q: An object moves along a straight line with its position measured relative to a fixed point O.Its…

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Q: For y = f(x)=x² - 6x + 3, find dy and Ay, given x=3 and Ax=0.2.

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Q: A company determines that its weekly online sales, S(t), in hundreds of dollars, t weeks after…

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Q: A tank contains 1000L of pure water. Brine that contains 0.05kg of salt per liter enters the tank at…

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Q: f(x, y) x² + y² - 1, (x, y) = (0,0). Applying the definition of continuity, explain if f(x,y) is…

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Q: Problem 7. Find a parametrization of the curve of intersection of x = cos(z) and y = sin(z) from (1,…

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Q: Sam borrows $2000 from a bank at an interest rate of 5% and pays back the loan continuously at a…

A: Loan amount = 2000 interest rate =5% = 0.05

Q: Suppose that is in the third quadrant (so that 77 < 0 < ³7) and tan(0) = 5.0. Compute cos(0). Enter…

A: Given;  tan(theta)=5.0.

Q: Suppose that f(x) is a degree three polynomial function such that f(-4) = 0, f(0) = 0, f(5) = 0 If…

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Q: The total weekly revenue of the Country Workshop in manufacturing and selling its rolltop desks is…

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Q: Graph the following piecewise function and give an explanation why the graph is discontinuous at the…

A: Here we have to plot a graph.

Q: 1 3 2 1 To find the blue shaded area above, we would calculate: ·b [ f(x)da Where: a = f(x) = 2 3…

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Q: Let f(x) = ln f'(x) = 8x + 4 7x 2

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Q: Let C be the positively oriented square with vertices (0, 0), (2,0), (2, 2), (0, 2). Use Green's…

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Q: Distance Between Two Cruise Ships Two cruise ships leave port at the same time. Ship A sails north…

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Q: The following quadratic function is given: f(t) = 5t²-7t + 25. i) ii) Use first principle to find…

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Q: Find an equation of the plane. The plane that passes through the point (-2, 1, 1) and contains the…

A: Topic = 3D Geometry

Q: Find the distance from the point s (−4,1,2) to the line x=9t​, y=4t​, and z=4t.  The distance is d =…

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Q: A rich uncle wants to make you a millionaire. How much money must he deposit in a trust fund paying…

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Q: Given cost and revenue functions and C(q) = 112q + 44000 and R(q) = -3q² + 3000q, how many items…

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Q: A producer and distributor of gift cards produces a boxes of cards per day at an average cost C'(x)…

A: given  C¯(x)=6x+100002x+400(a)  for produce 200 boxes put x=200

Q: 2. Subtract f(x) from f(x+h).

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Q: 2 f(x) = x² +1, (0; 2π), T = 2л.

A: we have to find the fourier series forf(x)=x2+1 in [0,2π]

Q: in solving the problem. Directions: Find the dy/dx by implicit differentiation. X^2 + y^2 = 100 X^3…

A: We can solve the given problem by using the implicit differentiation

Q: A tank is full of water. Find the work (in ft-lb) required to pump the water out of the spout. Use…

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Q: A spherical balloon is to be deflated so that its radius decreases at a constant rate of 15 cm/min.…

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Q: nd all zeros of f(x) eparated by commas. = x³ - 4x² + x - 4. Enter the zeros

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Q: Compositions of Functions In Exercises 41-44, find (a) fog, (b) gof, and, if possible, (c) (fog)(0).…

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Q: 15. Find the area of the figure below which has three 75.0 mm diameter holes drilled out. 784mm оо…

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Q: Find the limit of f(t): = 55t+ sin 6t 9t + cos 6t as t approaches - c.

A: