Find the derivative: f(x) = (4 sin x + 8 cos x)tan -1 X

Q: Solve for the value of C in the equation: O A. 1 OB. 2 O C.3 O D.4 O E. None of the Choices alt + dx…

A:

Q: Evaluate the following integral using trigonometric substitution. S dx (x²-36) 3/2 " X>6

A:

Q: 1. Given that lim f(x) = −1 and lim g(x) = 8, find the following limits. x-3 (a) lim (2g(x)-4f(x))…

A: This question can be solved using the concept of limits.

Q: Obtain the differential equation whose general solution is y = C₁ + c₂e³x. OA. B. U O y" - 3y' = 0…

A:

Q: Find the general form of f if f'(x) = 10f(x).

A:

Q: Obtain the differential equation whose general solution is y = C₁ + c₂e³x О А. y" - 3y' = 0 OB. 3y"…

A: the given  general solution  y=c1+c2e3x⇒y=c1e0(x)+c2e3x

Q: The integrating factor (IF) of the equation y' - 2ycot2x O A. sin2x O B. cot2x O C. Lnsin2x O D. E.…

A:

Q: If f(x, y) = 64 - 8x² - y², find fx(1, 2) and fy(1, 2) and interpret these numbers as slopes. fx(1,…

A: F(x,y)= 64 -8x^2 - y^2

Q: 16. Find the limit of the following rational function as (a) x-∞o and (b) x--co. -2x²-3x²+2 7x³+2x²…

A: Limit

Q: The integrating factor (IF) of the equation: (2x³y² + 4x²y + 2xy² + xy4 + 2y)dx + (2y³ + 2x²y +…

A:

Q: The integrating factor (IF) of the equation y' - 2ycot2x OA sin2x OB. cot2x OC.Lnsin2x OD. CsC2x OE.…

A:

Q: b) Find the area of the region described. The region inside the rose r = 2a cos 2β and outside the…

A:

Q: Solve for the value of C in the equation: O A. 1 (2xy4ey + 2xy³ + y)dx + (x²y4eY - x²y² - 3x)dy = 0…

A:

Q: † (OM_ON) - . If = -3, O A. e5 U O E. e-5 y5 y -5 then what is the integrating factor? None of the…

A:

Q: If f(x) = f'(x) = = f'(4) = 3 tan x, then -sin(x) - 3 sec²(x) COS X >

A: we need to find out the derivative for the given function

Q: Sketch the region bounded by the curve x 2 = y and the line x = volume of the solid generated by…

A: solution:-the region bounded by y=x2-2 & x=y+2revolving around y=1

Q: . Consider the point (x, y) lying on the graph of y = sqrt(x - 3). LetL be the distance between the…

A: Given data:- The given equation is, y=x-3

Q: Which of the following equations can be made into a linear differential equation?

A:

Q: 13. Suppose that lim f(x) = 13 and lim g(x) = -7. Find the following limits. X-4 X-4 a. lim…

A:

Q: Solve for the value of C in the equation: dy − (y + xy5)dx = 0 when y(0) = 1 - A. 1/4 B. 1/2 C. 3/4…

A: Find integration factor first as it is linear differential equation

Q: Question 29 If O O (OM dy O O j A. 5 - ly -5 ƏN ON) 1/2 = -5/201 əx y then what is the integrating…

A:

Q: dy Solve for the value of C in the equation: + ycotx dx O A.-5 OB. 5 OC.-4 O D. 4 O E. None of the…

A:

Q: Evaluate the following integral using trigonometric substitution. x² 441-x² S dx

A: ∫x2441-x2dx

Q: p(x)=3x^3−x^2−8x−25 k=3 Use synthetic division to determine if the given value for k is a zero of…

A: The given polynomial is  P(x)=3x2-x2-8x-25  check whether k=3 is a root of the polynomial or not.

Q: A (B) f(x) is continuous at.x=3 D lim f (x) exists x-3 (C) f(3) exists Based on the graph above,…

A:

Q: a -- In words, describe the curve F(t) = (2 sint,e',2 cost) for 0<= t <=6 . Be sure to give enough…

A:

Q: The voltage V in a simple electrical circuit is slowly decreasing as the battery wears out. The…

A:

Q: Which of the function is not an exact equation of the first order? OA. (ey + ycosx)dx + (xe³ + sinx…

A: See this solution in below.

Q: Which of the following equations is NOT an exact equation? | OA. (2x sin y + y)dx + (x² cos y + x)dy…

A: Exact differential equation A first order differential equation M(x,y)dx+N(x,y)dy=0 is called an…

Q: The integrating factor (IF) of the equation y' - 2ycot2x = 1-2xcot2x - 2csc2x

A:

Q: Use part one of the fundamental theorem of calculus to find the derivative of the function. -√³x 5 y…

A:

Q: What is the value of k so that the differential equation (y³ + kxy4 − 2x)dx + (3xy² + 20x²y³)dy = 0…

A: Given data:- y3+kxy4-2xdx+(3xy2+20x2y3)dy=0

Q: Which of the equations below is a second order nonlinear differential equation? O A. B. 2 x²y - (1 -…

A:

Q: Determine the set of points at which the function is continuous. 1 + x² + y² 5 x² - y² F(x, y) = = D…

A:

Q: Find the area of the region that is bounded by the given curve and lies in the specified sector. r =…

A:

Q: Which of the following is a non-homogeneous function? tan³y/x xLnx − xLny - xy + y² (y² + v²)3/2 43…

A:

Q: Which of the following is a non-homogeneous function? O O tan³y/x | xLnx − xlny x³ - xy + y² (y² +…

A:

Q: 8. Find the limit of f(x) = lim f(x)= 4- 818 (Type a simplified fraction.) lim f(x) = 8118 (Type a…

A:

Q: ating factor (IF) of the equation: - 4x²y + 2xy² + xy + 2y)dx + (2y³ + 2x²y + 2x)dy = 0 e of the…

A: We will find upon multipication which factor make above differential equation exact .

Q: Use synthetic division to determine if the given value for k is a zero of this polynomial. If not,…

A: By using synthetic division method the solution of given problem is as follow

Q: Which of the function is not an exact equation of the first order? O A. (ey + ycosx) dx + (xey +…

A: To find the non exact equation.   Option c and d are correct

Q: 111 Solve for the actual solution of y''' = 2x + 1 when y(2) = 1, y'(2) = − 4, y''(2) = 7 X 12 6 X 4…

A:

Q: Which of the equations below is a second order nonlinear differential equation? O A. 2 ¯\x²y - (1 -…

A:

Q: What is the standard form of this linear equation in one variable: (y + 1)dx + (4x − y)dy = 0? None…

A: Given (y+1)dx+(4x-y)dy=0 Multiply both sides by 1(y+1)dy (y+1)dx(y+1)dy+(4x-y)dy(y+1)dy=0…

Q: (a) If y=f(x) = 7e²+3x² - 20x-5, find the derivative f '(x).

A: given that,   y=f(x)=7ex+3x4-20x-5,   find the derivative of f(x)? formula:   ddx(xn)=nxn-1

Q: what is rational function ?

A: Relational number Our connection is number three. As you'll see that number is specific to our…

Q: The integrating factor (IF) of the equation: (2x³y² + 4x²y + 2xy² + xy4 + 2y)dx + (2y³ + 2x²y +…

A:

Q: Obtain the differential equation whose general solution is y = C₁ + c₂e³x. O A. y"-3y' = 0 3y" - y'…

A: Topic-differential equations We are given,y=c1+c2e3xWe know thatddxeax=aeax

Q: Solve for the value of C in the equation: dy − (y + xy5)dx = 0 when y(0) = 1 A. 1/4 B. 1/2 C. 3/4 D.…

A:

Q: Which of the following equations is NOT a variable separable differential equation? A. 2xydx + (x² +…

A: To find the equation is not variable separable.