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

Q: Find the general solution of the ODE. d'y dy +3. dx² dx Stre

A: Given d2ydx2+3dydx=5x+xex

Q: Evaluate: 2 sinxcos³xdx is equal to 0

A:

Q: If 10 fro A True B) False f(x) dx = 17 and 8 Lof(x) d f(x) dx = 12, then 10 ["fo f(x) dx=5

A: ∫010 f(x)dx = 17 ∫08 f(x)dx = 12 ∫810 f(x)dx = 5

Q: 1= sin√xcos√x √x A) None Зл B 256 Зл C 512 3 D 256 3 E 512 -dx is equal to

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: Question +² + 1 and g(x) = 2 between x = 2 and x = 3. If R is rotated Define R as the region bounded…

A:

Q: Determine the derivative of the function g(x) = ex^2 - e(2x-5). Do not simplify your answer.

A:

Q: Q2/B) Solve the following differential equation by using homogenous D.E method dy dx = 20

A:

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

A: Given,  f(x)=ex

Q: t'dt √4+1² 19 dt

A: We have to evaluate ∫02t34+t2dt.

Q: Find the area of the region lying between the inner and outer loops of the limacon r = 1-2 sin θ

A: I am attaching image so that you understand each and every step.

Q: A payment of $25,000 is due today. What three equal payments, one in 2 years, one in 4 years, and…

A:

Q: Q3.If f(x,y)=sin(x-3y) + sin(x1 find: af 2x and af dy

A: We can find partial derivative with respect to 'x' and 'y' .

Q: S (x - 8)dx x (x + 5)²

A: see below the answer and calculation

Q: y" + y = tanx

A:

Q: xp 11. 1. f, dxx -X

A: Let's solve  given integral.

Q: 4. Being careful to allow for parts of the curve being both above and below the x-axis, determine…

A: This question is related to definite integration, we will solve it using given information.

Q: A plane contains the point A(-1,2,5) and has direction vectors (2,-1,3) and (-3,1,5). Which of the…

A: Given:   Point : ( -1 , 2 , 5 ) Vectors : ( 2 , -1 , 3 ) and ( -3 , 1 , 5 )

Q: fxe-*dx= 303 blow Sie f sin (In y)dy =

A: Integration by parts : ∫u·v dx = u·∫v dx - ∫ddxu·∫v dx dx

Q: (D³ - 3D²D + 3)y = 0

A:

Q: 18. ydy 5-y

A:

Q: The difference equation given by A(yt - Yt-1) can be written as

A: Given

Q: Given that f is a differentiable function with f(3, 4) = 8, fx(3, 4) = 1, and f,(3, 4) = −1, use a…

A: We have to find the value of function by linear approximation.

Q: 12. 4 CSC X cot² x dx

A: Given problem:-

Q: 1 f(x) = (2x³ + 6) ³

A:

Q: dx 2. √ 9x² + x³² 12.

A:

Q: Define Q as the region bounded by the functions f(x) = x and g(x) = in the first quadrant between y…

A:

Q: ܐܐ 19. dz 'z(nz5

A: Solution is done in step 2

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: 11. fel/x²di .3 X хр

A: Here, to evaluate: I=∫e1x2x3dx

Q: solve the equation :- y'(t) = y(t) [a-y(t) ] ₁ y(0) = a/2, 970

A:

Q: 50 [" ( ax³ + bx² + cx) dx = 2b = 25 150 x ²6 x²dx -50 0 A) True B False

A:

Q: 1. Find the area of the region bounded by y = x^2 + 2x -6 and y = 3x.

A:

Q: f(x, y) = x³+y³-300x - 75y-3

A:

Q: What is the change of y with respect to x of the function s(x) = (3x¹ + 9x³)(x² - 6x +9) ? -9x²…

A:

Q: 5. In another state, license plates are formed using 6 symbols, any of which can be a number of a…

A: We know, There are 26 letters A, B, C, . . . , Z and 10 numbers 0, 1 , 2 , . . ., 9.Therefore we…

Q: Which condition shows the correct application of the chain rule?

A:

Q: y" + 4y= cos²x

A:

Q: 4. f In (2x + 1) dx =

A:

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

A:

Q: P af af Q3.If f(x,y)=sin(x-3y) + sin(x) find: and əy ax

A:

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

A:

Q: Consider the solutions Y(t) of with a, b, d constants and a, b>0. Calculate lim y(t). t-x Hint:…

A: This question can be solved using the concept of linear differential equation and limits.

Q: y dy Find S √y+2 A(√3+2-5) (5√3+2+y+24) + C B (√y+2-5) (5√/y+2¬y+24) + C 3 Ⓒ²(√x+2-5)(-3√x+2+y+21) +…

A:

Q: A payment of $700 is due in 3 years, and $5,000 is due in 5 years. What single payment made today…

A: Solution of given question is written in below steps.

Q: Derive : y = (5x-2) (2x + 3) - 1

A: I am going to solve the problem by using some simple calculus to get the required result of the…

Q: 149. Determine the real number a such that vectors a = 2i +3j and b = 9i+aj are orthogonal.

A:

Q: Given that dx [2²: = missing steps = [ √x + 2 Re-write the integral will all the missing steps. du =…

A: Rewrite the integral with all missing steps

Q: If 10 f(x) dx = 17 and (A) True (B) False #free f(x) dx = 12, then 10 Sofo f(x) dx=5

A:

Q: 10. X dx

A: