2. Given that y = (a + bx)e-* where a and b are constants, show that +2 +y = 0 dx2 dx

Q: Differentiate d dx y = 11x4 + 3 - (1₁x² + 3) =

A: As we know that

Q: If x²y + 3y* = xtan(y) + 2x d²y Find the value of dx²"

A:

Q: Evaluate Sdx dx where A = 5x²-3x+2 and B = x³ - 2x². B

A: Evaluatedxwhere A = 5x2-3x+2B = x3-2x2i.e.

Q: dy If y = (x +4)(x-9), then dx Select one: a. dy = 8x14 – 20x3 dx %3D b. dy = 8x7 - 20x° dx %3D C. =…

A:

Q: 1-7ӕ + 3 | dx 4.

A: To evaluate the integral: ∫1-7x+x3xdx. Solution: Evaluating the integral.…

Q: Differentiate y = 3e2x/(1 + x2.)

A: y=3e2x1+x2

Q: Find - 6x+1 x² +1 -dx.

A:

Q: 1. f4x-³ dx -3

A: Find the integral

Q: 2. [x² √x + 1 dx

A:

Q: 4. 16x – 2x2 – 23 dx -

A:

Q: x2+1 - dx x4-x²+1

A:

Q: d.x 2x2 +3x + 1 0. 2.

A:

Q: X 3- Ssin ² x dx ។

A:

Q: y = In( sech2x)

A: The objective of the question is to find the derivative of the function y = ln(sech^2(x)).

Q: Solve for d2y/dx2 for x = u2 - 3 and y = 4u3 - 2u

A: Given x=u2-3 and y=4u3-2u. To find d2ydx2. Solution: We have, x=u2-3 Differentiating the given…

Q: 2- Show that: -1 xb-1 In x dx b2

A: See the attachment

Q: 4. f 30x²5x³+3 dx e

A:

Q: Show that: -1 xb-1 In x dx b2 2-

A: we use integration by parts

Q: S (x – 3x + 7x + 9)dx %3D

A:

Q: Determine an expression for expression for 3(y-2)³ − x² = 4x − 6. dx

A: Solving the problem by finding the value of the problem by finding the value of the derivative.

Q: 3 = 4- 2y + - dx

A: The differential equation is,   The figure below represents the vector field of the differential…

Q: If y=8x3+2x2+5xy=8x3+2x2+5x, then d2y/dx2=

A:

Q: dx 2 0, x + x+ Vx + Vx +.. #mathiratti

A:

Q: 20. Find f2x/(5x-3)dx

A:

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.