dr = 3, find dt dA when r = 5. dt Let A be the area of a circle with radius r. If

Q: QUESTION 2 Use differentials to estimate v8.99 + (8.99)² correct to two decimal places.

A:

Q: Find dy/dx, where y is defined as a function of x implicitly by the equation below y = Arctan…

A: Given     y=tan-1(sec(3x))+π(cot(2x)

Q: Find the differential of the function. y = theta3 sin(9theta)   dy=?

A:

Q: dy Given: y= tan x Find dt dx when x =- m and dt = 2 m/s 3

A:

Q: The radius r and height h of a right circular cone arerelated to the cone’s volume V by the equation…

A: Given Volume of cone isV=13πr2hwhere r is radius and h is height and h is constant .

Q: *show work*

A: Find dy/dx.

Q: Find the differential of the function. y = (2+cos?)1/2 dy=?

A:

Q: Find the total differential, given: (b) \theta = arctan (y/x)

A: Let us consider the function z=f(x,y)  The partials derivative are obtained as…

Q: x =1+Int, y=r°+ 2; t=1

A:

Q: a - Find h (Stet sinh t sint dt)

A: The objective is to find ∫te-3tsintsinhtdt It is known that, sint=et-e-t2isinht=eit-e-it2…

Q: Find the total differential. w = = x?yz° + sin(yz) dw =

A: In partial derivatives, the total derivative approximates the function with respect to all of its…

Q: dy dx Given y=x³ - 2× and = 3. Determine the value of dt when X=2. dt

A: Differentiate the equation y=x3-2x with respect to t. y=x3-2xdydt=3x2dxdt-2dxdt=3x2-2dxdt

Q: da Given that at - t = 5a?t, find using implicit differentiation. dt da dt

A: We will find out the required value.

Q: Given that x and y are functions of time, find the indicated rate of change. dx Find when x = 4, y =…

A:

Q: 2x g(x) = |VI+t? dt 1+t2 dt %D

A: To find the derivative

Q: Find the differential of each function. (a) y = tan(V5 dy = 1 - v2 (b) у 3 1 + y2 dy =

A:

Q: Use Euler’s method to approximate the indicated function value to 3 decimal places, using h =   0.1.

A: Use Euler’s method to approximate the indicated function value to 3 decimal places, using h =   0.1.…

Q: A 25-foot ladder is leaning against a vertical wall (see figure) when Jack begins pulling the foot…

A:

Q: Find the differential of each function. (a) y = etan(nt) %3D dy = te tan (Tt)sec?(rt) 2. secʻ(nt)…

A:

Q: The radius r and height h of a right circular cone arerelated to the cone’s volume V by the equation…

A: We have given thatthe radius r and height h of a right circular cone are related to the cone’s…

Q: find the general salution of ly-3y12)de = xdy,

A:

Q: Use the differential dz to approximate the change in the function z (shown in the image) as (x, y)…

A: Given that:   The given function z = f (x, y) moves from the point (1, 1) to the point (1.03, 0.95),…

Q: (Hw) ex Test for Exactues ? (ext? + ax) dt+ (2tx* +zt)dx -.

A:

Q: L{S t? cos t dt}

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the 7th question.  Please…

Q: Find the total differential du. 1. w = y tan a? – 2xy

A: To find the total derivative

Q: The current in an electric circuit is given by the equation di Ri +L==0, dt - %3D where L and R are…

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: The radius r and height h of a right circular cylinder arerelated to the cylinder’s volume V by the…

A:

Q: dy given the equation a + y° dx = cos y. Use implicit differentiation to determine dy dx ||

A:

Q: Find the differential of each function. (a) y = tan(3t) dy =

A: We have given  y= tan(√3t)  We have to find the differential equation.

Q: H.W H find the degree of Precition. O F(x) = X

A:

Q: dw Jse the chain rule to find dt where w-x+y,x sint + cost y = cost- sint.

A:

Q: Suppose that the radius r and area A = pai r2 of a circle are differentiable functions of t. Write…

A: Given, Radius = r Area = A= pi*r^2

Q: Find for the equation below. dy dt

A:

Q: Find the differential of each function. (a) y = tan(v 5t) dy = 5- v2 (Б) у- 5 + v2 dy =

A: Use the basic concept of derivative and chain rule than simplify.

Q: dy Find dt y = (t sin t) dy dt

A:

Q: th² (t) В V = 2

A:

Q: Find the differential of each function. (a) y = tan V3t dy = (b) y = 1 + v2 dy =

A:

Q: Find the derivative of y with respect to t. 1 5 0<t< 8 y = sec 815 dy dt II

A:

Q: Find dy/dx by implicit differentiation. VTy = r'y+55 %3D dy/dx = %3D

A: Calculate dy/dx

Q: y=√x Find dy/dt, given x = 4 and dx/dt = 3 Find dx/dt, given x = 49 and dy/dt = 8

A: We have to find dydt given x = 4 and dxdt= 3 Find dxdt, given x = 49 and dydt = 8

Q: dx(t) If the PSD of X(t) is Sry(0). Find the PSD of - dt

A:

Q: The velocity of a particle moving back and forth on a line is y = ds/dt = 6 sin 2t m/sec for all t.…

A: given the velocity of a particle moving back and forth on a line is y = ds/dt = 6 sin 2t m/sec for…

Q: Differentiate f(x) | Vt + sin t dt.

A:

Q: Find the indicated derivative: d/dt ( * )

A:

Q: dR Q5:-The velocity of a particle moving in space is particle position as a function of t, if R= 2i…

A:

Q: Find the differential of each function. (a) y = tan 3t dy =

A:

Q: Given y is the square root of x. Find dx/dt when y=2 and dy/dt= 1.75

A:

Q: Find dy/dx if y = J' V1 + ² dt. Explain the main steps in your calculation.

A:

Q: Integrate to find the length of the curve. 8 S = 2 - + 4t dt 4 + 8 2t ++) dt = (? +t ln(t) 1 II

A:

Arc Length

Arc length can be thought of as the distance you would travel if you walked along the path of a curve. Arc length is used in a wide range of real applications. We might be interested in knowing how far a rocket travels if it is launched along a parabolic path. Alternatively, if a curve on a map represents a road, we might want to know how far we need to drive to get to our destination. The distance between two points along a curve is known as arc length. 

Line Integral

A line integral is one of the important topics that are discussed in the calculus syllabus. When we have a function that we want to integrate, and we evaluate the function alongside a curve, we define it as a line integral. Evaluation of a function along a curve is very important in mathematics. Usually, by a line integral, we compute the area of the function along the curve. This integral is also known as curvilinear, curve, or path integral in short. If line integrals are to be calculated in the complex plane, then the term contour integral can be used as well.     

Triple Integral

Examples: