Find the following integrals using substitution. -1 1. fx sin xdx. 2. fcot x In (sin x) dx.

Q: Given function f (x) = x3 − 12x + 2, (a) find the intervals of increasing or decreasing (b) find…

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Q: 6. A fisheries biologist is stocking fish in a lake. She knows that when there are n fish per unit…

A: The average weight of each fish is:Number of the fish is n

Q: Differentiate. y = In (4x² - 7x+5) y' =0

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Q: Nû 4 - x X X dx

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Q: Write a polynomial f(x) that satisfies the given conditions. 1 Polynomial of lowest degree with…

A: *to find,the polynomial f(x) which satisfies the condition given in question.*given,f(0) = 3.

Q: Determine the equation of the tangent to the graph of y-²-4-√x at the point (4,8). a) y=-7x+36 b)…

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Q: Find the length of the spiral r=0², 0≤0≤√21. The length of the spiral is (Simplify your

A: Consider the curve

Q: Let F(x) = f(xf (x²)). Suppose that ƒ(4) = 6, ƒ'(4) = 1, and ƒ'(12) = 5. Find F'(2).

A: Given, .Given,  f(4)=6, f'(4)=1 and f'(12)=5.

Q: 5. Given: y = cos(x), x =,dx = −0.02 (a) Find the differential dy. (b) Evaluate dy for the given…

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Q: Find the equation for the tangent plane to the surface 4x2+10y2-z=0 at the point (2,1,26)

A: 1. Calculate the gradient of the surface at the given point (2, 1, 26). The gradient is a vector…

Q: Find and simplify the derivative of the following function. f(x) = 25xe x -X The derivative of f(x)…

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Q: purchases a new car for $21,550. He makes a $6000 down payment and finances the remainder thro tized…

A: We have to find the monthly payment, amount and interest.

Q: 1. Let f be the function defined by f(x) = ln(2+ sin x) for ≤x≤2. a) Find the absolute maximum and…

A: The given function  for .The aim is to find the absolute extreme values and the inflection points.

Q: Find the linear approximation of the following function at the given point a. f(x) = sinx, a - ㅠ ▬ 2

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Q: A boat is pulled into a dock by a rope attached to the bow of the boat and passing through a pulley…

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Q: 3. In the theory of random motion of particles the following formula shows up: 2²/sin-¹ (√²) F(t) =…

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Q: According to a study, a vehicle's fuel economy, in miles per gallon (mpg), decreases rapidly for…

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Q: Find the eigenvalues of the matrix -40 -18 2 -8 -18 -14 -8 -18 -14, Enter the eigenvalues as a list…

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Q: Compute the curl and divergence of the vector field F(x, y, z) = (1, 2², 2yz). 1+x² Is F…

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Q: The position vector of a particle is r(t). Find the requested vector. The acceleration at t=2 for…

A: given

Q: Consider the following equation. cos (y) = 27 Use implicit differentiation to determine an…

A: Given equation, We know,

Q: A plane P contains two intersecting lines given by T₁ = (1, 1,0) +t(1,-1,2) T2 (2,0, 2) + s(-1,1,0).…

A: A plane P contains two intersecting lines given by…

Q: 2 y³ 4. Solve y' +-y X X² = using the following technique: A Bernoulli differential equation (named…

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Q: For the polynomial, determine its standard form, degree, coefficients, leading coefficient, and…

A: Given:- 5x + x4 - 3Standard Form is given by Standard form :- x4 + 5x - 3

Q: Q8 Find the set of intervals for the following functions (a) f (x) > 0 (b) f(x) = 0 (a) f(x) < 0 (b)…

A: we are given graphs of wo functions and we are to find on what intervals are those functions…

Q: If a rock is thrown vertically upward from the surface of Mars with velocity of 15 m/s, its height…

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Q: 2. On what intervals is the function increasing and decreasing? On what intervals is the function…

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Q: (b) logą (3x - 5) = 4

A: The given equation .The aim is to solve the equation.

Q: Solve for x. 3x = 22 Select the correct choice below and, if necessary, fill in the answer box to…

A: The given equation is

Q: -. Find dy and Ayat x = 8 with X he exact answers.

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Q: 4. Find the following limits. If the limit does not exist, write DNE and explain why. If the limit…

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Q: Find the derivative of the function. e Su -5u e y = e 5u <-5u + e

A: Quotient rule:

Q: 5. Recall that y = sec-¹x (with domain x ≥ 1) means sec y=x and 0 ≤y</2 or T ≤ y ≤ 37/2. Use…

A: To prove

Q: Find an equation of the following ellipse, assuming the center is at the origin. Sketch a graph…

A: The standard equation of an ellipse with the centre at origin is

Q: The region bounded by the given curves is rotated about the specified axis. Find the volume of the…

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Q: Use the differential dy to approximate Ay when x changes from x = 2 to x = 2.08. y = √√3x - 2 Enter…

A: Since you have asked multiple questions, we will solve the first question for you.If you want any…

Q: Write an equation for a line perpendicular to y = 5x - 4 and passing through the point (10,-7) y=

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Q: Given the demand function D(p) = √100 - 3p, Find the Elasticity of Demand at a price of $17 At this…

A: Elasticity,E(p) = Where D(p) is the demand function.

Q: Find the first partial derivatives of the following function. f(x,y) = 3xy³ + 1 =

A: By treating one variable at a time and other as a constant, we can find the partial derivative.

Q: Prove the statement using the ε, δ definition of a limit. lim x->2 (x^2-1)=3

A: =3

Q: 8 3 Evaluate S -dx. 10 9x 4

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Q: dw dt ne derivative where w = xyz, x = 5t³, y = 3t¯1, and z = 6 |z=6t-2 1

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Q: Write equation of line in slope-intercept form containing these two points: (-6,3) and (2₁1)

A: Given points are (-6,3) and (2,-1).

Q: Find the angle of intersection between the curves: y² = 4x and 2x²=12-5y at (1,2) to three…

A: Angle between the two curves is given by

Q: Given F(1) = 1, F'(1) = 1, F(2) = 3, F'(2) = 7 and G(2) = 1, G′(2) = 5, G(3) = 6, G′(3) = 2, find…

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Q: Use a calculator to evaluate each of the following. Give the answers correct to four decimal places.…

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Q: Set up a double integral in polar coordinates to find the volume of the solid bounded above by…

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Q: Find the absolute maximum and minimum values of the function over the indicated interval, and…

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Q: Solve e³t = 2000 for t. t≈ (Round to three decimal places as needed.)

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Q: Ihd an equation of the line tangent to the curve y = An equation of the tangent line is 5x 2 x +4 at…

A: Here we will solve it on finding the slope at x=4 after that we will use the formula of equation of…