Let y=ln(x^2 +x+2).  a)  Find the critical number(s) of the function f(x). b) Find the absolute maximum and minimum values of f(x) on the interval [-2,2].

Q: The general solution to the DE in the initial value problem (IVP) (y" + 8y' +16y = 0 y(0) = 1 y'(0)…

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Q: List all the primes between 20 and 40 in increasing order (in the form 2,3,5,7,9,11). A/

A: I am attaching image so that you understand each and every step.

Q: cent Round to nearest (4 decimals) Do Not Round until final answers Use the appropriate interest…

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Q: A baseball diamond is a square with side 90 ft. A batter hits the ball and runs toward first base…

A: Given that side of the square =90 ft.runs with the speed =27 ft/s.Solution :the distance covered by…

Q: [3] Find dy for the curve given by: 4x -x²y³ = e5y +9y

A: We can find the derivative by using the implicit differentiation.

Q: Part C. Find the √√x-5 8). x-15 1 9). +3+ + √x + 10

A: Topic = Function

Q: Q= (a) Find the point that is a distance 0.1 from the point P = (5,6) in the direction of v = (1,…

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Q: Let Find dy || ¹. y = f(x) = arcsin In 7x. dy dx

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Q: Determine whether the Mean Value Theorem can be applied to f on the indicated interval. If the Mean…

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Q: If lf Ŕ(t) = et cos tỉ – et sin tj Find the velocity and acceleration vectors.

A: To find the velocity and acceleration vectors for the given position function.

Q: Find the linearization. L(x) of f(x)=x² +1/x a+x= 1₁

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Q: H.W: Solve the following equations.... x Ben Bruden denken. . Berd... 4 X dyr X² 3.4).d.x.=.a.. T

A: 3) xy'+(1+x)y=e-x. 4)xdy+(x2-3y)dx=0.

Q: Find dy if y = tan-¹ (In(4x)). [A] 1 x(1+(In 4x)²) [B] 1 1+(In 4x)² [C] 4 x(1+(In 4x)²) [D] 4 1+(In…

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Q: sin(theta/2) -1 =0

A: Given query is to find the angle.

Q: The auxiliary equation of y"" - 4y" - 4y' + 16y = 0 is r34r²4r + 16 = 0. The auxiliary equation has…

A: Given; f(r)=r3-4r2-4r+16 , [-0.75,3.75].

Q: Using the Second Derivative Test, where applicable, find all the relative extrema of f(x) = 12x³ −…

A: Let's find relative extrema of given function.

Q: ax-1 = 81 solution set =

A: Given query is to find the value of x.

Q: Find the transform of the given function by use of a table. f(t) = 5t sin (5t) + e-st cos (t) A…

A: Given : f(t) = 5t sin(5t) + e^(-5t) cos t

Q: f(x) = cos 2x - 2 cos x on [0, 2π]

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Q: Find the equation of the tangent plane to f(x, y) = exy + xye¹-x at (0,1).

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Q: Find the Wronskian of the given pair: e²tsint, e²tcost 0 1 cost O e^-4t O e^4t

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Q: 6) a) Σ k=1 Determine whether each of the series below converges or diverges and explain your…

A: The given series is (k!)3/(3k)!, k from 1 to infinity.

Q: Please snow your answer to at least 4 decimal places. 4x Determine the gradient of f(x, y) = eª*…

A: Given, f(x,y) =e4xsin(4y)    Find gradient at (x,y)=(1,2)

Q: Let-202²-11zy + 3y²-672-36y - 39 = 0. dy Use partial derivatives to calculate at the point (-3,-2).…

A: Derivate the given equation with respect to x and then put the given point.

Q: Consider the initial value problem Suppose we know that y(t) → 0 as t → ∞. Determine the solution…

A: We need to solve D.E.

Q: 1. Evaluate the following expressions. Round your answer to 4 decimal places. a) log, 17

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Solve the boundary-value problem y" – 12y' + 36y = 0, y(0) = 8, y(1) = 0. Answer: y(x) = Note: If…

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Q: Calculate the integral of f(x, y) = 4x over the region D bounded above by y = x(2 - x) and below by…

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Q: Consider the following integral. Sketch its region of integration in the xy-plane. 0 LL 9-x² 6xy dy…

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Q: 1+t² e. y' = tye-t

A: We need to determine D.E. is separable or not.

Q: 2x²-5x-10 (x+2)(x² −4) dx

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Q: Find g'(0) if g(0) = cos 0 sin 0. [A] cos²0 [B] cos²0 + 1 [C] cos²0 sin²0 - - [D] sin²0 [E] sin²0 +…

A: As we know that; The Product rule: f·g'=f'·g+f·g' Use the common derivatives.…

Q: 7. Solve the exponential equation. Simplify your answer. Give an exact answer. a) 72x+1 +2 = 15

A: We can solve the exponential equation in the below steps.

Q: Use logarithmic differentiation to find the derivative of the function. y = (In(x)) cos(8x)

A: Please see the below picture for detailed solution.

Q: Find the linear approximation of the function f(x)= = √x at a= 1, and use the linear approximation…

A: NOTE: Refresh your page if you can't see any equations. . the given point is x=1 so the point on…

Q: Question 3 Find the transform of the given function by use of a table. f(t) = e4t 1 (A) F(s)= S + 4…

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Q: 1. Given [x² +1, 2x, x ≤ 1 x > 1. Is f differentiable at x = 1? Is it continuous at x = 1?. f(x) =

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Q: The following integral is an improper integral. (a) Explain why it is improper, (b) determine…

A: The following integral is an improper integral. (a) Explain why it is improper, (b) determine…

Q: S ex 2x (e²x + 8e*+7) 3/2 -dx

A: NOTE: Refresh your page if you can't see any equations. . .....................(1) substitute…

Q: A ball is thrown in the air from the top of a building. Its height, in meters above ground, as a…

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Q: Determine the least possible degree of the polynomial function shown. The least possible degree…

A: Let's find least possible degree of given polynomial function.

Q: 7. Use the chain rule to solve each problem: θω (a) Find for w= x² + y² + z², where x = st, y მs s =…

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Q: If f(4) = 11, f'is continuous, and f(6) = Submit Answer fºt f'(x) dx = 19, what is the value of…

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Q: dz/dt is incorrect

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Q: Determine all equilibrium solutions and classify as stable, semi- stable, or unstable. dx dt a. b.…

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Q: 2 Evaluate the following Integral - Find the partial fraction decompe √x3-3x² dx =

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Q: G. Let C be the curve defined by R(t) = (2e²t - 3,1-e²t, 2e²t). i. Find a vector equation of the…

A: Let C  be the curve defined by R→t=2e2t-3, 1-e2t, 2e2t.If the arc on C from the point P-1, 0, 2 to…

Q: 3. For Z= xtanxy,evaluate Zyy

A: The given function Z=x tanxy We have to find Zyy.

Q: 2x - 4 Find f ' (x) using the definition of the derivative: f ' (x) = lim h>0 f(x+h)-f(x) / h

A: Given query is to find the derivative using definition.

Q: Select the correct answer below: 6x² ln x-3x²+3 2 x ln² x 2

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