The sides of the rectangle below change according to = 1, = 34. What is dx/dt at the instant when x = 4 and y = 3? [Hint: 22 = x? + y²] %3D

Q: dy xe dx to

A:

Q: Evaluate 1cos ax dx and 1sin ax dx, where a is a constant.

A: We know that, ∫cosθdθ=sinθ+C           ⋯⋯1∫sinθdθ=-cosθ+C     ⋯⋯2 (a) We have, I=∫cosaxdx Let us…

Q: (a) 2-1 dx

A:

Q: Evaluate dy/dx at x = 2.5, correct to 3 significant figures, given y= (2x^2+3)/In 2x

A:

Q: [2 ln (x)+1] dy in yty cosy %3D dx

A:

Q: Find the derivative of the given function. y=cos(e^-5theta^3)   dy/dtheta=

A:

Q: d t In(t)dt} dx 3

A: We will find out the derivative of given function using fundamental theorem of calculus.

Q: dy Find the value of at t = 1 if dx? Vt2 + t, y = t2 + 3 x = 4

A:

Q: EXAM Q1-If x= cot- VE, y =;, find dy dzy dx' dx2 at t = 2. t+1

A:

Q: dy y3 , У (0) : 1 dx 1– 2xy2

A:

Q: Find dy/dx by implicit differentiation. VIY = r°y+66

A: givenxy=x5y+66diffrentiating by implicit method on both sideddx(xy)12=ddx(x5y+66)

Q: If x2 + y? = 169 and dy/dt = 5, find dx/dt when y = 12. (Enter your answers as a comma-separated…

A:

Q: Integrate the following using ~2 x+1 2. dx

A: ∫12x+1xx-1dx

Q: Find dy/dx and d²y/dx². For which values of t is the curve concave upward?

A: x = t2 + 1 y = et - 1 dy/dx = dy/dt ÷ dx/dt

Q: Restate this question in terms of dV /dt and dh/dt: At what rate is water pouring in if the water…

A: Restate this question in terms of dV /dt and dh/dt: At what rate is water pouring in if the water…

Q: xe* dx Jo (1+x)

A: Given                                            I=∫01xex1+x2dx now,…

Q: - 16y? – 16x – 16y = 0. dy at the point (3, dx ves to calculate

A:

Q: Find dy/dx by implicit differentiation. x2 = y? + 5 y' = %3D

A: To Determine: dy/dx by implicit differentiation.…

Q: dy dx

A:

Q: Use Romberg's method to compute dx 1+x? correct to 4 decimal places by taking h= 0.5,0.25 and 0.125.

A: AS PER OUR GUIDELINE WE ARE SUPPOSED TO ANSWER ONLY ONE QUESTION. KINDLY REPOST OTHER QUESTION AS…

Q: Find e dx approximately using Simpsons rule with n 10.

A:

Q: This is a calc 3 question    change the order of integration to dx dy dz

A: The given region of integration is bounded by all three axis and the plane:  x + y + z = 4.

Q: arsualuate the faltowmg integgal dx 4 Sin?x

A:

Q: Find the values of dz/dx and dz/dy at the given point

A:

Q: y = log, Vx? +1

A:

Q: dy dx=? 3.

A:

Q: Given the function y = x* e* , find dty dx for x = -1. %3D

A:

Q: a) How is ds/dt related to dx/dt if y is constant? ds/dt=___(dx/dt)

A: Consider a function S with variable x and y as constant. S=fx+ywhere, fx=function with x as…

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

A:

Q: The integrating factor of 3xdy + 3y dx is

A: given differential equation: 3xdy+3ydx=0 Remember :  A differential equation of the form…

Q: Given y=−3cosx, what is dy/dx?

A: y=-3cosx

Q: The heat transfer rate of the rocket engine is given by: dT Q = -kA dx

A:

Q: Given that xyt – 6 = 0, find dy by implicit differentiation. - %3D dx? dy dx?

A: A detailed solution is given below

Q: dy Differentiate implicitly to find dx 7xy + 1 = 0 dy %3D dx

A:

Q: th² (t) В V = 2

A:

Q: –1 dx

A: Solve the following

Q: /hat is the value of dx at the point (1,0) if y = In(x² +y²)?

A:

Q: 4-3x dy dx X,

A: its a multiple integral based question.so 1st we integrate with respect to y and then with respect…

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

A: Calculate dy/dx

Q: Find the value(s) of dx at y= 1 given that x²y+y² = 5. only В only 2

A:

Q: Find dy dx? at the following point using implicit differentiation: Va + Vỹ = 1, (1,0)

A:

Q: with x=sec t and y=e". Then the value of dz evaluated at dt If z=tan In t= 0 is equal to (Correct to…

A: Given function z=tanln4x2y with x=sect and y=e2t Substitute the x=sect and y=e2t in the given…

Q: calculate the derivative.

A:

Q: Differentiate y=arccos(e^(3x)) dy/dx=____________

A:

Q: Find dy dæ? by implicit differentiation when xy + 9y = 12 dy dx?

A: xy+9y2=12 We need to find d2ydx2 by implicit differentiation.

Q: x' - 4xy + y = 4 %3D

A: Given,          x2-4xy+y2=4

Q: A 15 ft ladder leaning against a wall begins to slide. How fast is the top of the ladder sliding…

A:

Q: Q3. Change the order of integration and evaluate * * dy dx.

A: To evaluate ∫04∫0xdy dx using the change of the order integration. From the limit of integration the…

Q: 2. 3t2 (t3 + 4)5 dt 3. 5x2 1- х3аdx

A:

Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.