Assume that x and y are both differentiable functions of t and find the required values of dy/dt and dx/dt. y = √x (a) Find dy/dt, given x = 4 and dx/dt = 6. dy/dt = (b) Find dx/dt, given x = 49 and dy/dt = 2. dx/dt =

Q: Let's practice on how to complete the square because this will help us to identify whether the given…

A: As per guidelines if multiple questions are posted we are allowed to solve only 1st question... for…

Q: (x+3)dx 10. ·S 4x² + 4x³+x²

A: A detailed solution is given below.

Q: Assume that x and y are both differentiable functions of t and find the required values of dy/dt and…

A: We can solve this as follows:

Q: dy = 26² Q2/B) Solve the following differential equation by using homogenous D.E method dx

A:

Q: Show that the differential form in the integral is exact. Then evaluate the integral. (1,2,3) Jazy…

A:

Q: Determine the area of region by y = x^2 + 4x and the y - axis

A: Area between the y=x^2+4x and y-axis is unbounded .  So, we will find the area bounded by the region…

Q: Sanna and Obadia argued about the definition of L e-x 1 dx - Sanna split the integral as -X e [54 dx…

A: We need to explain integral split.

Q: SET-UP a triple integral that will solve for volume of the solid S bounded by the sphere x² + y² +…

A:

Q: If f'(x) > 0 at x = c, f(x) at x = c is

A:

Q: Find the absolute maximum and minimum values of the function f(x) = cos²x-3sinx on the interval…

A: Given function, f(x)=cos2(x)-3sin(x) We know that, Suppose that x=c is a critical point of fx then,…

Q: EXAMPLE 1 lim x+1 X-1 SOLUTION Since lim 2 In(x) = 2 In(1) = = x → 1 we can apply l'Hospital's Rule:…

A: Here we have to find the limit of the function.

Q: Q1/B) Find the length of the cardioid curve: r = 1+ cose

A: A detailed solution is given below.

Q: Jonathan invested $240,000 to purchase a home. After 14 years, he sold the home for $320,000.…

A: The given problem is solved below in detail.

Q: 20. S dr √3-4r-r²

A: On solving this we will get

Q: f(x) = (6x² - 2x+1)^

A:

Q: For items 22-23: The equation of a curve is y = 6tanx. 22. What is the slope of the tangent line…

A:

Q: 18. S sin xdx 2-cos² X

A: The given integral is: I=∫sinx2-cos2xdx    ...1 As we know the common integral; ∫11-x2dx=sin-1x+C

Q: For the following exercises, use the second derivative test to identify any critical points and…

A:

Q: (2x + 3y - 1) dx - 4 ( x + 1) dy = 0

A: Explained below

Q: O C. Z= (sin O D. Z= (cos + i cos Write the complex number 9-9√3 i in exponential form. z= (Simplify…

A:

Q: y = (2x − 1) (x + 4)

A: To evaluate and to solve the function using the product and quotient rule of differentiation.…

Q: An open-box (top open) is made from a rectangular material of dimensions a = 8 inches by b = 6…

A:

Q: What is the derivative of y = (-3x²-x+4)e5 ANSE

A:

Q: 2.2 INTEGRATION OF RATIONAL FRACTIONS 16

A:

Q: Read, analyze and solve for the following. Express your answers as decimals rounded off to two…

A:

Q: -f(x)=√√5x² +2

A: Please see the answer below.

Q: 4. 13x²-1 3 X-X -dx

A:

Q: Determine the third order MacLaurin's polynomial for f(x) = ex.

A: Given,  f(x)=ex

Q: e Sc (4x + 3√y) c Evaluate figure. ds where C is given in the accompanying CH 1- (0,0) y=x O (1,1) X…

A:

Q: əx ду Əw aw x+y)+x²³ sec show that x +yay əx Ex: If w = y³ tan-¹ x²-y², x4-2xy³ Lemma: If w = f(g(x,…

A:

Q: Calculate the centroid coordinates of quarter circle (x² + y² = a*) in the quadrant, use Cartesian…

A:

Q: 2. fx²5-x' dx

A: ∫01x25-x3dxapply u substitution;take, u = -x3;du = -3x2-du3=x2then our equation can be written as…

Q: Find the gradient field of the function g(x,y,z) = 8xy + 6yz + 8xz. Vg = (Type your answer in terms…

A: This question is based on gradient of function.

Q: 9. J et dx 10. 4лr² dr

A:

Q: Find the derivative of f(x) = √5 - 4x. To enter √a, type sqrt(a). f (2)

A: The objective objective is to find f'(x).

Q: One of the correct steps to evaluate A B) None Ⓒ [+ + [ 1².40-16.4040] -S de cos 40d0 + [ 140 + 1 =…

A:

Q: Suppose and are non-zero, parallel vectors. Which of the following could not possibly be true?

A:

Q: Given cost and price (demand) functions and C(q) = 115q + 43000 and p(q) = -2.3q + 900, what price…

A: We have, Marginal profit (MF) = Marginal Revenue (MR) - Marginal Cost(MC)

Q: Which equation shows the correct derivative of the equation y = 2x² + 14x + 5? Oy = lim- 4th + 2h² +…

A: On solving this we will get that

Q: QUESTION 13 Is this statement true or false? An infinite sequence (a) is convergent only if lim a, =…

A:

Q: 3. fx² √9-x² dx

A:

Q: Suppose that an accelerating car goes from 0 mph to 58.6 mph in five seconds. Its velocity is given…

A:

Q: (5x²+4)

A: ddx15x2+43

Q: 9. If a rock is thrown upward on the planet Mars with a velocity of 10 m/s, its height (in meters)…

A: We need to find velocity.

Q: An inner-city revitalization zone is a rectangle that is twice as long as it is wide. The width of…

A:

Q: Solve the IVP. y" + 2y + 5y = 3 sin 2x y(0) = 1, y'(0) = 0

A:

Q: 1/A) Replace the polar equation by equivalent Cartesian equation r2cose + 2sino

A:

Q: Question Define R as the region bounded by the functions f(x) = around the x-axis, what is the…

A:

Q: Use Matlab Commands to solve the following exercises: Excercisel: a= b= Find i. 5a + 2b ii. |3a -…

A:

Q: A curve is given by the equation y = ln (2³+¹). x5

A: