Use lim f(x) XIC = 4 and lim g(x) = = X-C - 5 to find the limit. lim ([(x)]²+ (x-6)g(x))

Q: Simplify the following: (3q - q-¹)² a. -9q² - 6+q² b. 9q² + 6-q-² C. 9q² - 6+q-²

A: Given query is to simplify the expression.

Q: 6. Define h(r) = for all r. Prove that the function h: R→ R satisfies the € - 6 criterion on R.

A: In this question, we want to prove that the given function satisfy the given criteria on R.

Q: Expand, that is, perform the indicated operations on the differential operator D (xD+2)(xD-2)

A: Solution: The given differential equation is  (xD+2)(xD-2)

Q: If cot(x)=3/22 (in Quadrant-I), find  sin(2x)=

A:

Q: Answe

A: We have to determine the definite integral such that represent the area according to the given…

Q: Find the average value fave of the function f on the given interval. f(0) = 7 sec²(0/6), [0, 37] 2…

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Q: Identify the coordinates of any local and absolute extreme points and inflection points. y=x² + 18 X

A: we need to find out the coordinates of local maxima, local minima, inflection points.

Q: The rate of emission, E, in tonnes per year, of pollution from all factories in a certain country is…

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Q: f(x)=x-lnx

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Q: Given the vector-valued functions i(t) = et + et + 5tk (t) = 3ti + 3t²j5k d ind(u(t) (t)) when t =…

A: Given vectors:- u→t=e5ti+e-4tj+5tk v→t=3ti+3t2j-5k

Q: Find three positive real numbers whose sum is 36 and whose product is a maximu Enter the three…

A: Let three positive numbers are x,y,z

Q: Question Convert the equation r = 6 cos(0) + 3 sin() into an equation in rectangular coordinates.…

A: in polar coordinates   x=rcosθ   and  y=rsinθr2=x2+y2given  r=6cosθ+3sinθ

Q: ܠ -8 V64 - x2 1 1+Jx2 +y2 dy dx

A: To find:- ∫-80∫-64-x2011+x2+y2dydx

Q: 1. Evaluate the line integral where C is the half circle x² + y² = 1, y ≥ 0. 1²+y² ds

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Q: = L 3t dt. Then g' (2) equals Let g(x)= (Your answer should be a number.)

A: ∫xndx=xn+1n+1+cg(x)=∫x243tdt=3∫x24tdtdxndx=nxn-1

Q: Question 25 Determine the correct end behavior of f(x) = -4x³ - 2x²+2x+3 A B C falls to the left and…

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Q: Use Lagrange multipliers to find the point (a, b) on the graph of y = e5, where the value ab is as…

A: Let's find point by using Lagrange multipliers.

Q: 1. Let x = t-1, y = t² - 2t a. Eliminate the parameter and write an equation in rectangular…

A: To eliminate the parameter and form equation in rectangular coordinates

Q: Answer the following questions about the function whose derivative is given below. a. What are the…

A: Please see the below picture for detailed solution.

Q: 2. Find the complete solutions of the differential equation, = (x + 1)(x + 2), dx 3 and its…

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Q: 25-year old woman burns 200−20t cal/hr while walking on her treadmill. Her caloric intake from…

A: Given query is to find the calories decrease in 4 hours.

Q: Find all solutions of the equation in the interval [0, 2). cos 0= -5/7 If there is more than one…

A: We have to find the solutions in the given interval.

Q: 8. Find an orthogonal basis for the column space of the matrix to the right. An orthogonal basis for…

A: NOTE: Refresh your page if you can't see any equations. .

Q: Determine whether each series is conditionally convergent, absolutely convergent, or divergent

A: We need to find convergence.

Q: Suppose that the monthly marginal cost for firefighting portable water tanks is C'(x) fixed cost of…

A: To solve the following problem

Q: Determine the largest open intervals of the domain over which the function is A. Increasing B.…

A: From the graph  function is not increasing anywhere . Decreasing (-∞ , -3 ) ∪ ( 4 , ∞ ) Constant on…

Q: Let g be differentiable with g(-1) = 2, g'(-1) = -3, and a tangent line approximation of g(-1.024) =…

A:

Q: SUPPOSE THAT A TUMOR IN A PERSON'S BODY IS SPHERICAL IN SHAPE. IF WHEN THE RADIUS OF THE TUMOR IS…

A: To determine the rate of increase of the volume of the tumor.

Q: The marginal profit, in dollars from drilling a well that is x feet deep is given by P'(x) = 3. Find…

A:

Q: A What is the asymptate. graph of the function? [y=x+1/ B The graph of the function interrupts its…

A: We need to find intercepts and find how does function approach.

Q: Find the indicated partial derivative: Y Ə dy y + 2x = [

A: Given query is to find the partial derivative.

Q: Find the area of the surface generated by revolving the curve about the given axis. x = 9 cos(8), y…

A:

Q: An oil storage tank ruptures at time t = 0 and oil leaks from the tank at a rate of r(t) =…

A:

Q: The amount of trash, in tons per year, produced by a town has been growing linearly, and is…

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Q: Solve the differential equation. FD dy dx 3e * y = 2, x > 0

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Q: Use the formula for the binomial series: (1 + x) to obtain the Maclaurin series for 1 - 8x + 1 - 8x…

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Q: 11 = 2 A 1 as the sum of a vectory in W and a vector z in W+. 2 and 1₂ = a -13]. b , find a, b, and…

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Q: Use an appropriate test to determine whether the series converges. Σ k=1 k! 7kk

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Q: Use limit notation to describe the unbounded behavior of the given function as x approaches co. v(x)…

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Q: -2 0 1 O: 2 Find the absolute maximum of f(x)=√√4x2² on [-2, 2].

A: Here we have to choose the correct option.

Q: Let F(t) = (3t² + 5, 2e-5t, 3 sin(3t)) Find the unit tangent vector T (t) at the point t = 0. Round…

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Q: Find the indicated partial derivatives of: дz ?х дz ду || || z = ln(x2 + y3)

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Q: FIND y’’ OF y = square root of (x^2+1).

A: We need to find out the double derivative of the given function.

Q: A certain function f is given by the graph -8 50 Where are the horizontal asymptotes of f? 1. y = -3…

A: We have given graph of the function  From given graph  When x→-∞, y=-2 When x→∞ , y=3 So, horizontal…

Q: 4. Use the parameter t to write parametric equations representing a circle with center (2, -3) and…

A:

Q: If OHaganBooks.com were to give away its latest best seller, A River Burns through It, the demand q…

A: NOTE: Refresh your page if you can't see any equations. . the marginal demand function is given by…

Q: USE IMPLICIT DIFFERENTIATION TO FIND dy/dx. WITH THE GIVEN EQ’N: y^5+x^2 y^3 = 2 +x^2 y.

A: The given equation is y5+x2y3=2+x2y

Q: Suppose that the monthly marginal cost for a USFS approved wildfire water pump is C'(x) = 40x + 715…

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Q: Find the domain of y = log(4 - 3x). The domain is: Ox≤ A Ox> A Ox ≥ A 0x<A where A = 3x X syntax…

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Q: If csc(x)=8, for 90∘<x<180, then sin(x/2)=___ cos(x/2)=___ tan(x/2)=_

A: SOLUTION-