F(t) = 2 arccosvi A. F'(t) = - 1 2 4 B. F'(t) C. F'(t) = D. F' (t) = JE %3D 2vt-t2 Vt-t2

Q: Determine the instantaneous rate of change of the function πt ³ √x sin 2 f(x) = LV x3 1 + √t at x=2.…

A: Leibnitz integral rule.

Q: A particle is traveling upward and to the right along the curve y = ln x. Its x-coordinate is…

A: Given:

Q: We are given the function f(x,y)=sin(3x+2πy)+exy-π, and points A(π, 1), B(π + 1, 0). Find the rate…

A: Given function is, fx,y=sin3x+2πy+exy-π. To find the rate of change of f at A(π,1) along the…

Q: Find the Integration of: fn (3sint + esin t) cost dt In 3

A: Given that, ⇒                   y =∫π2π( 3sint +esint) costln3dt⇒                     find the value…

Q: A particle moves along the curve y = x^(3/2) in the first quadrant in such a way that its distance…

A: Let (x,y) is a point on y = x^(3/2)Distance of (x,y) from (0,0) is given by:

Q: Find the average rate of change of f(x) = cos x from 0 to π /2 .

A: Given: fx=cosx  0,π2

Q: Find partial derivative of dx for the function f(x,y) given below exp 2x. siny .(at the point (In2,…

A:

Q: dx 3. J TxVx-1

A: the given integral is: ∫dxxx-1 we have to evaluate the given integral.

Q: dx/dt of -ln(-cos t)-e^(sin t)

A:

Q: Find the maximum rate of change of the function f(x,y) = sin (xy) at the point (4,0) and the…

A: The given function is f(x,y)=sin (xy) and the point is (4,0)=(a, b). to find : Maximum rate of…

Q: 18 dx Integrate using trig. Substitution: S- x² V9– x²

A:

Q: (b) Use Romberg integration to compute dx 1+x correct to three decimal places.

A: Given: I=∫01 dx1+x  correct to 3 deecimal placesLet h=0.25,…

Q: Find the total differential. z = 10x"y3 dz =

A:

Q: Find the total differential dz ZzxeX+y

A: NOTE: Refresh your page if you can't see any equations. . take the partial derivative with respect…

Q: 6) dx X 3 Type 2 mproper integral 1-

A: We use Type II improper integral  Here at x=0 f(x) is discontinuous so we break the limit at x=0 If…

Q: A particle is traveling upward and to the right along the curve y = ln x. Its x-coordinate is…

A: Given a particle is travelling upward and to the right long the curve y=lnx. It is given that dxdt=x…

Q: Find maximum rate of change of f at the given point. f(x,y)=sin(xy), (1,0)

A:

Q: 3. Water is being poured into a 10 liter leaky container so that the volume of the water, V,…

A: A differential equation is an equation that contains functions and their derivatives.  A…

Q: A particle moving along the x-axis has velocity function v(t) = t sin t. How far does the particle…

A:

Q: ly 4% confident that the true po ation percentage of people that

A: The margin of error is the amount that is allowed for the error term to vary because of…

Q: A point moves along the parabola y = x² in such a way that the rate of change of x : kx, || dx dt…

A: Since dx/dt = 10 at x = 5, therefore 10 = 5k k = 2 Now, calculate dx/dt at x = 7. dx/dt|x=7 = 2*7 =…

Q: dy dx

A:

Q: What is the integrating factor of (y – cos² x) dx + cos xdy = 0?

A:

Q: (b)/ Use the Trapezoidal Rule with n = 4 to estimate (x' + 1)dx.

A:

Q: In integrating the function fx' In Sx dx using integration by parts, what would you choose for your…

A:

Q: Q2 Integrate by parts: ex sin x dx

A: find ∫exsinxdx we know, ∫u.vdx=u∫vdx-∫dudx∫vdx now, apply this on equation I=∫exsinxdx…

Q: 5. Find the rate of change of the distance D between the origin and a moving point on the graph dx…

A: Given: y=x2+7 then A moving point on the graph is: (x,y)=(x,x2+7) And dxdt=8 cm/sec We have to find…

Q: Let y tan(4x + 3). Find the differential dy when z = 3 and dx = 0.1 Find the differential dy when r…

A: y=tan4x+3

Q: Find the differential dy of y = tan x for x = π/4 and dx = −0.1.

A:

Q: Find dy/dx by implicit differentiation. x²y2 + x sin(y) = 4 dy/dx %3D

A:

Q: A particle moves along the curve y = x3/2in the first quadrant in such a way that its distance from…

A: Let w de the distance between origin and the particle at any time t. Given that, dwdt=11 Now by…

Q: Find the differential of the function. y = sqrt(1+ln(z))   dy=?

A:

Q: What is the instantaneous rate of change for α=arctan(2-r/r) at r=0

A:

Q: .A telegraph cable is made of an outer winding around an inner core. If x is defined as the core…

A: Using double derivative test to get max value of x

Q: 53. df = (x+ 1)ye"dx + xe*dy

A:

Q: In integrating the function fx cos(3x) dx using integration by parts, what would be your v?

A: Solution

Q: In integrating the function fx cos(3x) dx using integration by parts, what would you choose for your…

A: Let ,I=∫ xcos3xdxSubstitute  u=3xdifferentiate du=3dx⇒du3=dxI=∫ u3cosudu3I=∫ucosu9duTake the…

Q: Find dy/dx by implicit differentiation. 9x2 + y2 = 4 dy/dx = %3D

A: Topic:- Differentiation

Q: In integrating the function fx In 5x dx using integration by parts, what would be your v?

A:

Q: Find the total differential. z = ex tan(y)

A:

Q: Find dy/dx. x = 9/t, , y = Vte-t

A: topic - derivative

Q: Find differential of the function y = (x² + 3)°. dy = dx. When x = 4 and dx 0.05, compute the…

A:

Q: Find the total differential. z = 10x y10 dz =

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Q: Let y = tan(3x + 4). Find the differential dy when x = 4 and dx = 0.4 Find the differential dy when…

A: We know that, ddxtanx=sec2x We have,  y=tan3x+4 On calculating derivative with respect to x, we get…

Q: Suppose both x and y are functions of time (t). Find the rate of change of y with respect to t, that…

A:

Q: A new fast-food firm predicts that the number of franchises for its products will grow at the rate…

A: Given

Q: Find dy/dx. x = 6/t, y = Vte-t

A: The parametric equations are given by x = 6t  y = te-1 To evaluate : The expression of dydx

Q: 3. Estimate the value of the integral 1 dx (n = 4) using Trapezoidal rule. 1+ln x

A: The value of h in the trapezoidal rule is h = b-anh = 5-34h = 24h = 0.5 Form a table with the x…