Question 21 Find the equation of the tangent line to y = x = 1. at A y - Vi = - Vi (x – 1) B VE (x - 1) У — 2 (х — 1) 4 D y - V2 -(х — 1) =

Q: 1.1 Find all the points on the curve x²y² + xy = 2 dy if y = x sin() dx 1.2 Find

A: Note the result : The equation represent a equation of rectangular hyperbola .The points on the…

Q: Question 1 Consider the curve defined by 2y3 + 6x2y - 12x² + 6y = 1. dy 4х - 2ху (a) Show that dx x2…

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Q: Question 1 : Use Runge – Kutta's method of order four to find an approximate value of y for x = 0.2…

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

Q: 1. If an object moves with velocity v(t) = sin(t) + 3t and begins at position p(0) = 0, find the…

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Q: 1) Find the equations of the lines that are tangent to Y = 0.5(sin 2t) at the origin the curve COs…

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Q: Question 7 2²e"² sin(x²yz) Let f(x, y, z) 12 find dyəzə"x at the point (3, 0,0) 4 8.

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Q: 3:27 12.0 X. 49l ..l D Calculus College 3 of 10 (3) Find the equation of tangent to the curve given…

A: Given :  x=a3cos3Φ , y=a3sin3Φ  and  Φ=π4. Therefore, we know that the slope of a line is : dydx. We…

Q: 1. [10pts.] Find an equation of the tangent curve at the given point: x=1+t y=e; (2,e) 1/2

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Q: dy (a) If y = e° sin-1 (0) and z = e28 + cos-1 (0), find dx (b)Find the equations of the tangent and…

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Q: 4.1. Find the slope of the line tangent to r = 4 – 3 sin 0 for 0 = ™

A: The given question is based on the tangent and normal topic in which we have to find only the…

Q: Problem #1 Find 4x-5x2 +s dx Problem #2 Calculate f'(t) if fle)=3t°csct Problem #3 d4x-x+3 Calculate…

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Q: An object moves along the x-axis so that its position at any time t > 0is given by x(t) = cos(t2…

A: Given :                          x = cos t2+1      , t≥0To find velocity V = dxdt

Q: 1- find dy/dx as a function of x. y = sec (tan x) 2- find dy/dx etty = 2x + 2y %3D 3- find an…

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Q: Question 5 The Integrating Factor for the DE y dx = (ye-2x)dy is 2y -2y None of These

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Q: 31-32 Find an equation of the tangent line to the given curve at the specified point. 2x 31. y= et…

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Q: Question 2 Find an equation for the line tangent to the curve at the point defined by the given…

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Q: Question 8 Suppose that a biomass B(t) changes with respect to time t (hours) at the rate dB Vt +…

A: We have to find

Q: Question 12 The Integrating Factor for the DE y dx = (ye-2x)dy is None of These 2y -2y

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Q: Question:5 Differentiate with respect to x y = x* e* sinx Inx + xª

A: The given term is  y = xx ex sinx lnx + xe^x.

Q: 19. The slope of the tangent to the curve (x2 + y²)² = 4.x²y at the point (1, 1) is 3 3 (a) - () – 1…

A: We have to find slope of the tangent to the curve x2+y22=4x2y at the point 1, 1. We know slope of…

Q: EXAMPLE 1 (a) Find the derivative of r(t) = (4 + t4)i + te-tj + sin(2t)k. (b) Find the unit tangent…

A: Given data:     The given expression of the vector is: r(t)=(4+t4)i + te-tj +sin(2t)k.   (a) The…

Q: 16. If g(x) = x + 2 cos x, then the equation of the tangent line to the graph of g at x = is 3π 2 A.…

A: This is a basic application of derivative problem

Q: Question 25 dy The general solution of the DE dx cos²y is %3D A y= cos(x) + C

A: Given:- dy/dx= cos2(y)  To find:- General solution of given differential equation

Q: Problem 7.4. A particle moves along the x-axis such that the velocity is given by v(t) = 3t + cos(t)…

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Q: Question 6 af Given f = esec (#) -ya+y, find dy (#) sec² (=) ye NO -y+In (y)

A: Given :f=esecxy-yx+y

Q: Question 9 Let y = tan e find the differential dy of the function. O dy = e (r – 1) sec e- da O dy =…

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Q: 6. Find * : y- + 5)ao TK, (b) y = Sin 5x I+cos 5x dx

A: Solving the problem by finding the derivative.

Q: QUESTION 11 dz = = zP z1- -i (-e2 – 1)i e (e? + 1)i e (e? – 1) ei (e2 – 1)i e

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Q: Question 02: Solve with suitable condition d'y dx - = 0, where y(0)=2, y'(0) = 3, y" (0) =4, y" (0)…

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Q: 10. Find an equation of the tangent line at the point t = 1 for s(t) = In(8 – 4t).

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Q: (1)Find dy/dx when 3x2+3x3y - 5y3 = 20  dy/dx= (2)The slope of the tangent line to this curve at…

A: The function 3x2+3x3y-5y3=20. We have to find the derivative, slope of the tangent line at (2,2) and…

Q: A b. C find an equation of the tangent to the curve at the given point (T/6,1) 4 sin ² x y = + y =…

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Q: Question 8 Let y = tan find the differential dy of the function. O dy = e* (x² – 1) sec² \ e*"-1 dæ…

A: As we know that; The Power law: ddxxn=nxn-1 The Chain rule: fgx'=f'gx·g'x And ddxtanx=sec2xddxex=ex…

Q: 1. a) Find the equation of the tangent line to the curve given by F(t) = (cos(nt), t, 1 + t2), for t…

A: First we find r(2) and r'(2). Then find equation of tangent line to given curve r(t).

Q: Ev 2 x 2 [x²z dx - yx² dy + 2 dz along the curve C'shown in the figure. AZ 2

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Q: Question 7 OT 15, Step Correct Consider the function y 3x + 5x2 + 4x - 2. Find the differential for…

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Q: (a) e 20 sin(30) de (b) t sin(2t) dt 0.

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Q: Problem 4. Consider the function f : R² →R given by f(r, y) = y² – 2r². Find the directional…

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Q: Question 22 The solution for the initial value problem -sinx, y()=1 dy is 3D1 dx O a. y=-cosx+1 1…

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Q: 1. (a) Find an equation of the tangent plane to the graph of x² + y² + z² = 16 at (0, 2, 2√3).

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Q: * PROBLEM 4 a) Use implicit differentiation to find dy/dx of the function ху (x²y + 1)2 b) Evaluate…

A: a) Given function is  We differentiate both sides with respect to x

Q: Let C be the graph of the equation In(3y – 2e") = sinh (ma) - tan(y- 1). dy (a) Find da (b) Find an…

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Q: cos(5r)ő(1 – 3) dt = e sin(t)6(t – 2) dt =

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Q: Question 3 Consider the function f(r, y) = 2x + 4y² %3D and the curve y(t) = (sin t, cos t), te…

A: Introduction: For a given function fx,y and a curve rt=xt,yt, their composition is frt=fxt,yt. The…

Q: An equation of the tangent line to the curve y = sin(x) at x = 4n/3 is y = + -(х — 4п/3). An…

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Q: The curve with equation y= e* In(x- 1) has a stationary point when x = p. (i) Show that p satisfies…

A: Given- The curve with equation y = e-2x lnx - 1 has a stationary point when x = p. To Show- Show…

Q: Set C: Problem #6 Fina the equgtion of the line tangent tO FCx)= cas?x - sin² () at x = 2JL

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Q: 5. Find y' at the point (0, e) where xy² + In(x² + y) = 1.

A: Find y' = dy/dx At point (0, e)

Q: Question 10 [i[cosh:(2x²) – sinh ( 2x³) ]dt is equal to A © Sude xdx E None

A: Integration

Q: 9. Find the equation for the tangent line to f(x) = at *=-1 A)9x+25 y =-34 B)9x+25 y=-24 C)-9x+25y…

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