For the curve given by r(t) (-4t, 6t, 1 – 7t2), Find the derivative '(t) = ( -4 6 -14t Find the second derivative g"(t) = ( 0 -14 Find the curvature at t = 1 K(1)

Q: a. Graph the following system of equations. y = -3x y = x + 4 b. What does the graph show to be the ...

A: We have to Graph given system of equations after that we have to find its solutions.

Q: Find dy at x = -1 if y = u’ +5u – 4 and u = x² +x . dx

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Q: Which of the following is the formula for finding the distance between two points on the coordinate ...

A: The formula for finding distance between two points (x1,y1) and (x2,y2) is, d=(x2-x1)2+(y2-y1)2 Opti...

Q: 5. Find the domain (D), all asymptotes (VA, HA, or OA), and the holes (if any) on the graph of each ...

A: NOTE: Refresh your page if you can't see any equations. . to find the vertical asymptote, take deno...

Q: The monthly revenue R (in dollars) of a telephone polling service is related to the number x of comp...

A: Solution is written in below steps.

Q: if g(x) = fcx)-メ+ Find %3D (5) © D.g

A: Hope the D indicate the differential of the functions.

Q: "A Kite 65 feet above the ground moves horizontally at a speed of 6 ft/s. At what rate is the angle ...

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Q: 1. Find fe- cos(x)dx. 2. The following improper integral converges. Compute it using part 1. e* cos(...

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Q: (х+2)* x² – 4 dy 2y dx x? - 4 х —

A: Given  :        dydx+2yx2-4 = x+22x2-4

Q: 12x + 13x2 lim 13x3 - 7

A: limx→∞12x3+13x213x3-7=limx→∞x3(12+13x2x3)x3(13-7x3)=limx→∞(12+13x)(13-7x3)=(12+0)(13-0)=1213

Q: За + 25 — 5 Evaluate the limit: lim

A: Given query is to find the limit of the expression.

Q: If R is the region bounded by the lines y = x,y=0,x= 1, evaluate the dxdy double integral S by chang...

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Q: is an angle in standard position with T(-20, -21) on its terminal ray. Find sece O -29/21 -29/20 29/...

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

Q: 4. If ā= 3i - 2j and b=-5i- j, express 3 a -b in terms of i and j.

A: This is a vector problem

Q: (b) Find the instantaneous rate cf change of C with respect t i when x = 100, (This is called the ma...

A: Given function C(x)=5000+10x+0.05x2 Aim: (a) To find the average rate of change of C with respect of...

Q: 3.) y tanʼxdx +ln* ydy = 0 dy_ (y?+4) Inx In (y?+4)Y 5) dx

A: y tan2x  dx + ln4y dy = 0∫-tan2x  dx =∫ ln4yy dy∫(1 - sec2x) dx  = ∫ t4 dt   (where, t = ln y)Hence,...

Q: 3.2 2. 3t (t 8-4れt。75 ニ

A:

Q: sec 2 2 O tan´y dx = secx dy

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

Q: Perform the indicated operation and write the result in standard form. Select all values that are co...

A: Given the query is to the correct option for the given expression.

Q: V3 - 2 lim H:-4 5.

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Q: se the four-step process to find f'(x) and then find f'(1), f'(2), and f'(3). 8. f(x) = 1+ - (x) =

A: Topic:- derivatives

Q: 3. S sin? (2t) cos³ (2t) dt 4. ſ tan³(3x)dx

A:

Q: Using logarithmic differentiation fx) = x° [2x+ 3 (x*+1)4

A: NOTE: Refresh your page if you can't see any equations. . take log on both sides

Q: tan? y dx = sec2 x dy %3D

A:

Q: A rumor spreads through a school. Let y(t) be the fraction of the population that has heard the rumo...

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Q: x - yArctan | dx + xArctan ) dy = 0 %3D

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Q: 9. y'+ 2x y = x e*2 subject to IC: y(0) = - 1 10. (x + 1) y' + y = In x subject to IC: y(1) = 0

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Q: If $2,000 is invested at 7% compounded monthly, what is the balance after 8 years? $3,601.84 $3,490....

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Q: Explain how you would approximate the slope of the tangent at a point without using first principles...

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Q: - y=-2x + 2 6. у%3D-2х -2

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Q: Consider the sequence (") an = In ((n + 1)41 240 This sequence is not monotone for all n. Determine ...

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

Q: B. LIMITS Evaluate the following limits: z² + 4z – 12 EDIE 3. lim I² – 2x lim g (y) where,, [ y² +5 ...

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Q: Find the slope of the function's graph at the given point. 8 Function: 9(z) %3D Point of g is at (2,...

A: Slope of the tangent is obtained by dy/dx

Q: Find the unit tangent vector T, and the unit normal vector N for r(t) = at t = 1. Simplify your ans...

A: We need to find the  unit tangent vector T, and the unit normal vector N for t=1.Below find the solu...

Q: Consider the graph of 7x2 4x + 4y? – 5y = 100. - - - 4x + 4y? – 5y If the graph of 7x? stretched hor...

A: Topic:- calculus

Q: Find the first three non-zero power series terms of each of the two linearly independent series solu...

A: we have to find the power series of y"=xy

Q: An average of 40,000 people visit Riverside Park each day in the summer. The park charges $15.00 for...

A: given that, number of people =40000 ticket price=$15 and for each $1 increase in price,the park woul...

Q: y(2x³ -x²y + y³)dx - x(2x3 + y3 )dy = 0

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Q: Consider the given system. 2x + y == 0 Graph the inequalities on your graphing calculator, and fin...

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Q: 3n Find the equation of the tangent lines to the curve y = sin x at x = - T, 0, and 2 Graph the curv...

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Q: Find the slope of the function's graph at the given point. 8 Function: g(x) Point of g is at (10, 0....

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Q: 2. Find the polynomial f (x) of degree 4 whose graph is shown. Leave your answer in factored form. 1...

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

Q: The value of tan is undefined

A: Given that: tanπ2

Q: Disney+ Use the matrices below to perform matrix multiplication. 4 -5 11 4 6 5 B = D = 9. 1 %3D -9 0...

A: Please refer to the image below

Q: Consider two vector equations ℓ1 : ⟨x, y, z⟩ = ⟨3, 7, 4⟩ + t⟨2, 3, 1⟩, for some parameter t, ℓ2 : ⟨x...

A: Check the Ratio of direction ratios of both the lines. 

Q: sin r lim ,3 81.

A:

Q: Given T→(π)=⟨0,−4/5,3/5⟩ , find an original v→(t) function that looks like a circular spiral or cork...

A: Given T→(π)=⟨0,−4/5,3/5⟩ , find an original v→(t) function that looks like a circular spiral or cork...

Q: Find the derivative 1. y = Vx² – 5

A: Since you have asked multiple question, we will solve the first question for you as per our guide li...

Q: Evaluate the limit t3 – t lim t→1 t2 – 1

A: We have to find the given limit.

Q: Salve for x if Arc tan (1- x) + Arc tan (1 + x) = Arc tan

A: Our Aim is to solve for 'x' if tan-11-x+tan-11+x=tan-1x -(i)