5. Rewrite the expression as an algebraic expression in x. X cos( 1¹ (3)). H≤3 |x|≤3 (a) cos sin

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A: We can find the answers in the below steps.

Q: DERIVATIVE AS VELOCITY AND ACCELERATION Solve for the unknown/s 3. A particle moves horizontally…

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

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A:

Q: Solve (x5 + 3y) dx - xdy = 0. O 2y = x^5 + cx^3 O 2y = -x^5 + cx^3 O 2x = y^5 + cx^3 O 2x = -y^5 +…

A:

Q: Which of the numbers 1, 2, 3, 4, 5, and 6 are critical numbers of the function graphed below?…

A: Given,

Q: Find the derivative of the following functions. Whenever possible, express answer in factored form.…

A: y = ((x³- 2)/(x³ + 1))³ dy/dx =3( x³-2/ x³ +1 )² × [ ( x³ + 1)3x² - (x³ - 2) .3x²/ (x³ +1)² ] dy/dx…

Q: S 2 x (4-x²) 3/² хр

A:

Q: (5) A student used "U-substitution" 3 integral: S x² √√9- x² dx By using the following steps: Let U…

A: We need to find out the integration by using trigonometric substitution.

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A:

Q: Find the derivative of each function using the basic properties of differentiation. 1. f(x) = 5-7x…

A:

Q: 3. lim_ log₂ (x) x-15 4. lim (cos(x)-1)

A: answer 3 and 4 only Given :3.limx→15log2x4.limx→0cosx-1x

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A:

Q: If z = (x + y)e and x = 7t and y = 1- t², find the following derivative using the chain rule. Enter…

A:

Q: tan 2x lim 3 X-0 X + a 2 X sin bx X = 0

A: Topic:- calculus

Q: Find the derivative of the following functions. Whenever possible, express answer in factored form.…

A:

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A:

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Q: Let f(x)=xsin(x)/1+x. Find f'(pi/2).

A: We can find the answer in the below steps.

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A: Here, note that the domain of the given function f(x) is [-3,3] which are the x values for which the…

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A:

Q: Find the derivative of the following functions. Whenever possible, express answer in factored form.…

A:

Q: If f(x) = 2x + find f'(1), using the definition of derivative. f' (1) is the limit as x → of the…

A:

Q: Find the linear approximation of f(x)=√x when x = -27.

A: Linear approximation is an approximation of a general function using a linear function. It is useful…

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A:

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Q: If z = xy² and x = e sin(t), find the following derivative using the chain rule. Enter your answer…

A:

Q: Let f(x) f'(x) (6x-2)4 (5x2 – 4)6 . Compute f'(x).

A:

Q: Find the derivative of the following functions. Whenever possible, express answer in factored form.…

A:

Q: A railroad bridge in one city has a low clearance for trucks. An engineer standing 23 ft away…

A:

Q: A right circular cone with radius r and slant height / has surface area given by A = nr² + nrl. When…

A:

Q: Əf Əf Find and дх ду 2 f(x,y) = √x² + 3y2

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Q: Do NOT use the difference quotient, find the derivatives via formula. f(x)= 4√x7

A: To be found :  the derivatives via formula. f(x)= 4√x7

Q: 3. xlny + ylnx = 1 a. y = y = x Y + x x² In x-y y² ln y - x y' = O b. xlny + y yylnx+x ( 21 x y = y…

A: Given,

Q: Question 3 Let P(t) be a deer population (in thousands) of an ecological region t years after 2000.…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: =O 2. (6x+y²) dx + (2xy-3y²) dy

A: Given differential equation, (6x+y²)dx+(2xy-3y²)dy=0...(i) Comparing (i) with Mdx+Ndy=0 we get,…

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A:

Q: Find a. b. C. d. e. f. g. lim x-3 lim x0 lim x → 0+ lim x10 lim x2 f(x) h. f(2) f (x) f (x) f (x)…

A: We need to evaluate the following limit for the given graph of the function a. limx→-3fxb.…

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A:

Q: Eliminate A and B from x = A sin(wt + B). w being a parameter not to be eliminated. Ox"+w^2x = 0…

A: To form the differential equation.

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Q: P(w)=2w^2 -w +4 /√w *Differentiate the function

A:

Q: A differentiable function f(x, y) has the property that f(4,3) = 6 and fx (4,3) = 6 and fy(4, 3) =…

A: We need to find z.

Q: 13. Find the point (x, y) on the curve y = x² + 1 that minimizes the distance to the fixed poi (4,…

A: Given curve:- y=x2+1 We know distance between points x1,y1,x2,y2d=x2-x12+y2-y12

Q: Find the derivative of the following functions. Whenever possible, express answer in factored 3.…

A: y=(x^3-6x)(2-4x^3) apply product rule y=uv dydx=udvdx+vdudx

Q: Find the area of the region enclosed by the rose r = 14 cos 38.

A: Given, r=14 cos 3θ

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A:

Q: Straight line whose y and x intercepts are equal

A: Here is the solution:

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A:

Q: 1. Given the algebraic function x² − xy + y² = 3

A: Here is the solution:

Q: f(x)=xsin(x)/1+x. Find f'(pi/2).

A: Given query is to find the derivative.