12. For f(x) = x' +3, g(x) = x – 10, and h(x) = /x find f°g•h. %3D Gogo h\(x) = (~x - 10) +3 a. |3| (fogoh)(x) =x' +x-7+ x b. c. (fog•h)(x) = (/x -7) x' -7 d. (fogo h)(x) = %3D G•g• h\(x) = (x° +3) + (x - 10)-/I %3D

Q: 1 The derivative of the function y = cos V at z e = is equal to 4.

A:

Q: 1. Find the rate of y with respect to x at the point (1, 7) if 7y – ry = 4. dy da

A:

Q: When a vertical beam of light passes through a transparent medium, the reason that its intensity I…

A: We have to find What is the beam intensity at 15 feet below the surface.

Q: Use the Euler method with dx = 0.5 to estimate y(5) if y' = y2/√x and y(1) = -1.  What is the exact…

A: In the given question, it is asked to solve a differential equation using Euler’s method.

Q: 9. The anti-derivative of the function f(x) = e² + cost is (a) e²+ sinx+c (b) e² - tanz+c 10. 0.5(x…

A:

Q: 1. If z = 2xy – 3x²y and x is increasing at 2 cm/sec determine at what rate y must be changing in…

A: Z is neither increasing nor decreasing at the given instant. A function is said to be neither…

Q: 1 (5* )csch dy if Find dx 1. (а) y x>0. (ecosh 5x ) In Vx +1 d Show that for x 2 1, coshx- dx (cosh²…

A:

Q: Use the Euler method with dx = 1/3 to estimate y(2) if y' = y - e2xand y(0) =1.  What is the exact…

A:

Q: 4. Show that 2 s w (b) L(t sinh (wt)) (s² – w²)2 -

A:

Q: 11. Verify that wxy = Wyx for w = e* + x ln y + y ln x

A:

Q: 1- Evaluate: 2y sinx dy dx อน 2- If u = x² + ey², x = sin 2t , y = cost² find Ət

A: Above question is solved.

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: Find the most general antiderivative of f(x) = -3e" + 10 sec2 (x), where - < x < 2 Note: Any…

A: According to the given information it is required to calculate the antiderivative of the function:

Q: Find the linear approximation of f(x)=ln(x) x=1 and use it to estimate ln(1.1). L(x)= ln(1.1)=

A:

Q: What is the derivative 7 of y = (3x + 1)²? 21 dx dy = 6 (3x + 1)²¹ dx = dy 6 (3x + 1)² dx = 7 (3x +…

A:

Q: 1- for y= sech x is equal to: dx a) sech' x tanh x b) 3sech sech tanh x c)-3sech2x sechx tanhx

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

Q: 4- Find dy/dx for: d- y = /1+ sin³ (x5) e- y = 2(Va – 1)( f- y = cos³{sin(2x*)} x-2 x²+3x' %3D

A:

Q: If y = 4x³ + 2x² + 11, find the approximate value of y when x = 2.01, using differentials.

A:

Q: The general antiderivative determined by - x² - 3x +2 is dx

A:

Q: Suppose y = square root 2x + 1 where x and y function of t . A) if dx/dt =12 , find dy/dt. When x= 4…

A:

Q: fy = f(r), how do we define the differential dy

A:

Q: If f(x,y) = y2 ex + 3 ln (xy), find fxyy (1,1). fxyy (1,1) = ?

A:

Q: To use differentials to approximate V9. You would use x = and dx

A: Solis as follows

Q: 6. If f( x, y) = V x° + 1 y², estimate the value of f( 2.06 , 4.97 ) using the differentials.

A:

Q: Find for the following function: dx 1- y = log2 cosh(2x) 2- y = e(x*+1) 3- xy + x²y = 3 at x = 1 4-…

A:

Q: 1. Find the centered difference approximations of 0(h^4 ) for the first derivative of y=sin(x) +…

A: As per the policy, we are allowed to answer only one question at a time. So, I am answering the…

Q: 11) Find the antiderivative: f -3+6√x³ √√x dx

A:

Q: finel cly 0- ó cost +1nt) e e (cos Ø + Ssin ø)

A:

Q: find (x² – 2x + 1)e²* dx dx 9. 10. fun tan - y dy y dy 11. 12. sin- x sec² x dx 4x sec2 2x dx 13.…

A: Hello thank you for the question. We’ll answer the first question since the exact one wasn’t…

Q: d 1+ tanhx - Show that dx V - tanh x

A: To show: ddx1+tanhx1-tanhx4=12ex2 Simplfiying 1+tanhx1-tanhx,…

Q: 6. S(x) = e 05 (2 cos 2x+3sin 2.x) 7. , evaluated at x = 1 rad Find the indicated partial derivative

A: Given:   f(x) = e ^ (0.5x) * (2cos 2x + 3sin 2x)

Q: 4. For the given derivative, find the antiderivative that satisfies the indicated condition. f '(x)…

A: We have to find the anti derivative of the function or we can say that we have to integrate the…

Q: Let y=(x to the 2nd power +3) to the 2nd power . Find the differential dy when x=4 and dx=0.2…

A: Given,    y=(x2+3)2

Q: Q /Choose the appropriate derivative for this function y = (x+ 1)2* dy = 2* (x + 1)2" - In(x + 1) dx…

A: Explanation of the answer is as follows

Q: Use the Euler method with dx = 0.5 to estimate y(5) if y′ = y2/sqrt(x) and y(1) =-1. What is the…

A: Consider the formula used in Euler’s method.Also summarize the given data in the question.

Q: Solve using variaton of parameters or recuction of order (D²-2D+1)y = e" (e*+)²

A:

Q: y is a function of  x and the slope of the function is zero at x=10 then to determine that y reaches…

A:

Q: Q:: If In/x2 + y² =sec(), use implicit differential to proof the following: - -x-(r+y?). sec. tan…

A:

Q: 2. In each case, find the derivative d. (a) z = x³ – y² and x(t) = cos 2t and y(t) = e-3t, (b) z =…

A:

Q: (a) Find thẻ đéřivătivė. rivative. 1 y = In(x2 – 6) 3 dy dx (b) Find the derivative. 3 = INVX2 – 6…

A:

Q: 2- find dy/dx e2x = sin (x + 4y) 3-find an equation for the line tangent to the graph f(x) = x –…

A:

Q: 7. Given y = sinh(e* +tan (2x)-cos (x+1). Consider | dy (i) et 1 dx 1+e2x 1+4x 1-(x+1) dy (ii) ex 1…

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

Q: What is derivative d(y)/d(x) of "xsin(1/y^e)=(1-xy²)^½

A:

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: 2. If f(x, y) = 1/(xy), the marginal pdf of X is (log x)/y.

A:

Q: 10. Compute the central difference approximations of O(h^4 ) for the first derivative of y =cos(x) +…

A: Solution is below

Q: Let y=(x2+4)to the 4th power. Find the differential dy when x=3 and dx=0.3.... Find the…

A:

Q: 1- Cosh x dy + (y sinh x +e*) dx =0

A: