Assume the following: f(x) dx ce. ƒ(2) dx = 2, ª f(z) dx = 3, 9(z) dz = -1, and + [°²9(2) ² = 2, [ f(x) dx g(x) dx = 4.

Q: fx) D, f(쪽) -1, and f(플) %=D1, and COSX 3 f) = -1. Find S f(x) dx. %3D

A: Given that  f'x=cosxx, fπ2=-1 and f3π2=1find ∫π23π2fxdx

Q: Find for the following functions: - dx 3x2-4x+4 1) y = %3| Z

A: dydx is called the derivative of function y.Derivatives of polynomials are :→dxndx =…

Q: Find dy/dx without changing the form of the given function and answer must be in the simplest form:…

A:

Q: d (7) Vtan²s+ 21 dt = dx

A: Explanation of the answer is as follows

Q: I Solve the following FODF (x1)x*dy= (3x3y-xy +y²)dx

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Q: (x*y - 2xy) dy dx 2.

A:

Q: Determine the value of- dy - at (0,0) for the following expression: 3x² +2y = 3x – 2y dx 10.

A:

Q: dy 2- Find for the following function: dx А- у%3Dх*. сosx B- y= 2(secx)²

A: Given : A) y = x3·cosxB) y = 2secx2

Q: Find the second derivative of y = 6xcosx.

A:

Q: Let ƒ(x) = x3 - 3x2 - 1, x>= 2. Find the value of dƒ -1/dx at the point x = -1 = ƒ(3).

A: We will need inverse function theorem. Statement of the theorem is:

Q: If y is a function of x and y3 + y2 - 5y - x2 = -4, find dy/dx implicitly.

A:

Q: O Find (a) |VT-x)/x dx, (c) (4-x*y² dx. Ans, ía) 1/60, (/) x/2. (c) 31

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Q: a) Integrate the following functions i. (-2x² – 9x – 7)dx (4x* – 9)* (20x“ )dx. [-4e"dx ii. iii.

A:

Q: (c) Find the value of √a²-x² Sa giving your answer in terms of a. 1+ 2(x + y) x² + y² dx dy,

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Q: - [5√3x d dx

A:

Q: Differentiate implicitly to find d2y/dx2.   3y2−xy+5x2=5

A: Differentiate implicitly to find d2y/dx2.  3y^2−xy+5x^2=5

Q: Clearly explain why the following equation is true or false. f(x) dx S FEx) dx lim

A: When the range of integration is not finite then the integral falls under improper integral.  Hence…

Q: SSx = 172.5, SSY = 80.6, and ∑[(X – Mx) (Y – MY)] = 95.33, r =  A. .08. B. .01 C. –.81. D. .81.

A: SSx = 172.5 SSY = 80.6 and ∑[(X – Mx) (Y – MY)] = 95.33

Q: (x + 2y)dx + x dy = 0.

A: Differential equation.

Q: Find dy by dx when y is equal to 3x³-12x²+7x-19 divided by 4x

A: To find dydx when y=3x3-12x2+7x-194x. Solution: Power rule of differentiation states that:…

Q: 5x² + 3xy = 3y², find the derivative dy da. as a function of x and y.

A: Consider the equation

Q: Find y in terms of x given that (1+ x) = x²y and that y = 2 when x = 1. dx

A: The given differential equation can be simplified as shown below: (1+x)dydx=x2y     ⇒…

Q: Suppose thatƒ(x) = d/dx (1 - √x) and g(x) = d/dx(x + 2). find ∫g(x) dx

A: Given: fx=ddx1-xand gx=ddxx+2 To Find: ∫gxdx Concept: Integration is an inverse process of…

Q: Find the derivative. d. (in (5x? + 2))

A: We have to find out the derivate of given function

Q: a. (In(x² − 3x + 1)) = = b. — (In(ex + 5x)) = d a + (n (+)) = [ C. dx +1 Hint: Use properties of…

A: