1) State the vertical asymptotes of f(x)= a. x=6₂x=-2 b. x=6, x=2 1 x² - 4x-12 c. d. x=-6, x=-2 x=-6, x=2

Q: Use Lagrange multipliers to find the indicated extrema, assuming that x, y, and z are positive.…

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Q: 3) y" + 4y' + 4y = 0.

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Q: Write an equation for the transformed logarithm shown below, that passes through (3,0) and -5-4-3-2…

A: The graph is given as , Find the equation for the graph.

Q: Use the power series f(x) = In (1-x) = -for-1sx<1, to find the power series representation for the…

A: The power series fx=ln1-x=-∑k=1∞xkk, for -1≤x&lt;1 we have to find the power series for px=9x8ln1-x

Q: Given differential equation -3x yay"-4y' + 8y = e +8x² (D³ - 3D² 4D +8)y=e +8x2 Auxilary equation…

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Q: 1. Evaluate the double integral r²y dA, where D is the region enclosed by the x-axis and the…

A: We can evaluate the double integral.

Q: 10. (a) Construct the Taylor polynomial p3(x) of degree 3 for the function f(x) = 1/(2-x) around x =…

A: Solution is given below:

Q: If r(x) = -cos (x + 9) +7, determine the antiderivative of r(x). (Do not include the constant C'in…

A: In this question, we want to find the antiderivative of the given function r(x).

Q: If In a = 2, ln b = 3, and ln c = 5, evaluate the following: a² b²c4 (a) In = (b) In √a²b²c4 =

A: To evaluate the given expression.

Q: Find equations of the spheres with center (2, -3, 5) that touch the following planes. (a) xy-plane…

A: As per our norms we have to write one question at a time kindly repost remaining questions.

Q: The indicated function y₁(x) is a solution of the given differential equation. Use reduction of…

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Q: 5. It was noon on a cold December day in Tampa: 16°C. Detective Taylor arrived at the crime scene to…

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Q: Find f(x,y) and fy(x,y). Then find fx (2, -1) and fy (-4,3). f(x,y) = In 5x4 +8x²y²| fx(x,y)=…

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Q: - (D² +8D³² +16) y = _ sinx Ans: Y=as2x+ C₂ Sin2x + C3 Xcos2x + (4x sin2x - 1 9

A: The solution is given below

Q: 2 Determine the length of the curve = = t³, y: 31² 2,0 ≤t≤ √3.

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Q: Solve the given differential equation by undetermined coefficients. y" - 8y' + 16y = 12x + 6 y(x) =

A: The given differential equation is;  y''-8y'+16y=12x+6.

Q: Consider a pool shaped like the bottom half of a sphere, being filled at a rate of 25ft^3/min.the…

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Q: (a) Find an equation of the tangent plane to the surface at the given point. z = x² - y², (3, 2, 5)…

A: Since you have posted multiple questions. As per guidelines we"ll solve only  first question. If you…

Q: Solve the given differential equation by undetermined coefficients. y" + 7y' + 6y = 18 y(x) = || X…

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Q: Verify the identity. sin(x) + cos(x) = sin(x) cos(x) sec(x) + csc(x) sin(x) + cos(x) sec(x) + csc(x)…

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Q: Solve a part only

A: Given the function y=2-xx2 Here, student asked part a) only, hence we are answer part a) only.

Q: a b = A = B Note: Triangle may not be drawn to scale. Suppose a = 6 and c = 7. Find: B = b O A O

A: Solution: Given:  a=6,    and c = 7 Using Pythagorean theorem

Q: A swimming pool whose volume is 10,000 gal contains water that is 0.03% chlorine. Starting at t=0,…

A: Given: the volume of swimming pool = 10000 gal that contains 0.03% chlorine. at t=0  ,0.002%…

Q: The indicated function y₁(x) is a solution of the given differential equation. 6y"+y'- y = 0; y₁ =…

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Q: Determine the amount of material in grams that will be left after 55 days. The inital amount of…

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Q: Use the Laws of logarithms to rewrite the expression 3 (212. √/y13 in a form with no logarithm of a…

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Q: Diminishing Returns Jesaki Inc estimates that it will sell N(x) units of product after spending $x…

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Q: Find the surface area of the solid generated by revolving the region bounded by the graphs of y =…

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Q: 2. (x+y) dx + (3x + 3y − 4) dy = 0

A: The objective of the question is slove the given differential equation.

Q: Find the gradient of the function at the given point. Function Point f(x, y, z)=√√√√x² + y² + z² (4,…

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Q: Find the directional derivative of the function at P in the direction of v. 1 = √₂ (i+j) f(x, y) =…

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Q: 2ss" + (s')² = 0

A: we will solve the differential equation.

Q: Let f(t)= F"(t), with F(t) = 5t2 +t, and let a = 4 and b=7. Write the integral f f(t) dt and…

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Q: Solve the following ODES by Undetermined Coef D Ş 17 4X y - 16 y = 19.2 e + 60e, y(a) =ý (os. 4X -4X…

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Q: ∞ Determine whether the series (-1)"- n gent, or divergent. n=1 is absolutely convergent,…

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Q: Find f if f"(x)= e-sin z - 3 4√ f'(0) = 0, and f(0) = 8.

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Q: Find the equation of the level surface of the function g(x,y,z)=x^2+y^2+z^2-2x+4y-6z corresponding…

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Q: 1. 9x2 + 4y2 = 36 2.222² 쫑 = 1

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Q: Use Theorem 13.9 to find the directional derivative of the function at P in the direction of the…

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Q: Find a parabolic curve that would fit the following data. Let  y = a + bx + cx2. x      3    5…

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Q: Write the given differential equation in the form L(y) = g(x), where L is a linear differential…

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Q: Find an angle coterminal to  25π/3 that is between 0 and 2π

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Q: Find the Laplace Transform of f(t) = te cos(3t) (A) B D s+1 s² (s+ 1)² +9s² = ((5+1) ²+9) S s²…

A: This question is related to Laplace transform, we will solve it using given information.

Q: Estimate the area under the graph of f(x) = approximating rectangles and right endpoints. R₁ = 1 x²…

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Q: The function is not one-to-one. Delete part of the domain so that the function that remains is…

A: Here we have to find the inverse function.

Q: An exponential function f(x) = ab passes through the points (0, 3) and (3, 375). What are the values…

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Q: Determine csc(x) + cot (x) if tan x + sec(x) = 22/7. 27/12; 29/15; 24/18; 23/11

A: We can answer the question by finding the correct option as below.

Q: G 2. x²y" + 3y' - xy = 0

A: We need to determine singular points of D.E.

Q: -1 Range of f -4 -5 -6 O (c) Describe the relationship between the graphs. Domain of 1 -81 Range of…

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Q: In terms of limits, what does it mean for f to grow faster than g as x→∞? Choose the correct answer…

A: We need to choose correct option.