Find the general solution in powers of x of (x2-1) y" + 4xy' + 2y = 0.

Q: Evaluate the limit: tan (6x) lim x 0 sin(11x) + 12x The limit exists, lim x 0 The limit does not…

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Q: The graph of a function fis is shown below. k 16 5 4 m cu -6 -5 -4 -3 -2 -1₁. -2 -3- -4 -5 6 4…

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Q: Find the indefinite integral. (Remember to use absolute values where appropriate. Use C for the…

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Q: The letters A through E on the graph represent different time intervals. Use thom letters to answer…

A: Solve the following questions using graph.

Q: Solve the given initial value problem (3x + ye³/¹) dx - xe³/* dy = 0 y(1) = 3 y(x) =

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Q: Determine whether the Mean Value Theorem can be applied to f on the closed interval [a, b]. (Select…

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Q: Find the indefinite integral. J Step 1 cos 8x dx Observe that Step 2 Multiply and divide the given…

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Q: Find the volume of the solid generated by revolving the shaded region about the x-axis. The curve is…

A: The region bounded by curve ,

Q: Consider the function f(x) the difference quotient = 7 x²+1/ 3 4 -X-2. Compute f(xo+h)-f(xo) h

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Q: The graph of a function f is given. Use the horizontal-line test to determine whether f is…

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Q: If f(x) = 3x(sin x + cos x), find the derivative.

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Q: A function f(x) is said to have a jump discontinuity at x = a if: 1. lim f(x) exists. 210 2. lim…

A: Let To show that  has a jump discontinuity at  by calculating the limits from the left and right at…

Q: 1 10. Consider the region R bounded by y = x ++ and y = x - for x ≥ 1. (a) Sketch the region. (b) Is…

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Q: Find a formula for the sum of n terms. Use the formula to find the limit as n → ∞. lim n→∞ n i = 1 X…

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Q: Please show your answer to 4 decimal places. Suppose that f(x, y) then the maximum is =…

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Q: - A function f(x) = x² was reflected over the x axis and translated 2 units up. What is the equation…

A: The given parent function is

Q: Let r(t) = (et, et sin t, et cos t).  Find the equation of the plane that is normal to the curve at…

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Q: A spacecraft has acceleration r"(t) = , initial velocity r'(0) = and initial poition r(0) = (0, 0,…

A: GIven that a spacecraft has acceleration with initial velocity r'(0) = <2, 5, 1> and initial…

Q: Find the integral. √3x 31 Step 1 8x + 7 1-x² Split the integrand 8x + 7 V 1- x' | 31 J 8x + 7 dx…

A: Need to find the below integral∫8x1−x2dx

Q: Find the constant a such that the function is continuous on the entire real line. 4sin x X a - 4x a…

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Q: The Eiffel Tower, in Paris France, is approximately 324 meters tall. A camera is 85 meters from the…

A: The figure

Q: Use implicit differentiation to find an equation of the tangent line to the curve at the given…

A: By using implicit differentiation to find an equation of the tangent line to the curve at the given…

Q: Use differentials and the graph of f to approximate the following. (Round your answers to three…

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Q: A function f(x) is said to have a removable discontinuity at x = a if: 1. f is either not defined or…

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Q: Determine whether Rolle's Theorem can be applied to f on the closed interval [a, b]. (Select all…

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Q: Question 5 7 Let f (x) X The slope of the tangent line to the graph of f (x) at the point The…

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Q: The half-life of radium is 1690 years. If 80 grams are present now, how much will be present in 550…

A: Exponential Law of Decay is given as follows Where A is the amount after time t  is the initial…

Q: You deposit a lump sum Pin a tnast fund on the day your child is born. The fund earns 7.3% interest…

A: Rate of interest  r=7.5%=0.075future value  A=$ 600,000

Q: A rectangular package to be sent by a postal service can have a maximum combined length and girth…

A: A rectangular package to be sent by a postal service can have a maximum combined length and girth of…

Q: Consider the following. f(x) = (4x)² (a) Sketch a graph of the function f. 6 -8 -6 -4 -2 2 4 -2 2 N…

A: The given function

Q: 11. Find the exact area of the region bounded by the parametric curve x = cost, y = 2 sint; 0<t<2n.…

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Q: Could the function in the bottom plot be the derivative of the function in the top plot? Explain…

A: We have given two graphs and we have to explain if function in bottom plot could be derivative of…

Q: Strontium-90 is a radioactive material that decays according to the function A(t) - Ape 0.0244t,…

A: Since you have asked multiple sub parts in a single request so we will be answering only first three…

Q: The graph of f is shown. Evaluate each integral by interpreting it in terms of areas. y (a) 33 (c)…

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Q: Let f(x)=  x+2/1-x •Show that the function is one to one  • Find d f^−1(x)/dx at x=1/2 without…

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Q: se the Two-Path Test to prove that th Ollowing limit does not exist. Ov

A: We have to test the given limit doesn't exist.

Q: Complete the table by identifying u and du for the integral. [r(g(x))g(x) dx [ (tan(x))² (sec(x))²…

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Q: 4. dx -ydy - y² dx +xy dy =D X = 2 y=2

A: Compare this equation with,So here we have

Q: Find the values of m and b that make f continuous everywhere: 54+3x-² x+6 mx + b 4.24 +51 f(x) =…

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Q: Suppose an arrow is shot upward on the moon with a velocity of 61 m/s, then its height in meters…

A: given

Q: The population of a southern city follows the exponential law. Use this information to answer parts…

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Q: Find the derivative of: -4√x - 2 x6 Type your answer without fractional or negative exponents. Use…

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Q: Find the volume of the largest rectangular box in the first octant with three faces in  the…

A: Find the volume of the largest rectangular box in the first octant with three faces in  the…

Q: Write the expression as a sum and/or difference of logarithms. Express powers as factors. In…

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Q: Use the chain rule to find the derivative of f(x)=5(-9x¹⁰ – 5x⁹) ¹⁹ 10 19 You do not need to expand…

A: Given,

Q: xy Two resistors wired in parallel in an electrical circuit give an effective resistance of R(x,y)=…

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Q: 9. y X = yesc x T|3 y = √₂ ± √6 C = =

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Q: Compute the limit. Enter the number if the limit exists and N if the limit doesn't exist. lim…

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Q: 24. Find the x- and y-intercepts of the line that is tangent to the curve y = =√/² at the point (1,…

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Q: -8 -6 -4 -2 8 6 4 2 CH + -6- -8 16 X

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