Question No.06 A)Differentiate the following. f(x) = (x + 5)(x³ + 7x² – 9) (3x2 +4x) a)f(x) = (x* +5xª +e²) b)f(x) = (4x³ +x² + 9e°)-3

Q: Differentiate f(x) = 3 (√4x² + 2x + 7x+2) x+1

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Q: 6x-25x+8x+43x--8x-12 (3x4-11x3 +9x²-11x+6) (9x² +12x+16) + C(3x+2)+D 9x²+12x+16] Find f - [Ax+B x²…

A: Given integral is      (1) Its reduction is ∫Ax+Bx2+1+C(3x+2)+D9x2+12x+16dx We can write it as…

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Q: What is the domain of f(x) = √(x – 5) / √x  (√ means “the square root of”)?

A: Given: f(x) = √(x - 5) / √x let's get the numerator:√(x - 5)x-5≥0x≥5let's get the denominator: √x…

Q: (P) xp- (e) fx dx (1) √(2x² - 6² xp(x9

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Q: f (x) = x2 - 1 / x + 4  Find the following:   5) f (2x)  6) f ( a + k)

A: Given:-   fx =x2-1x+4   now, a. f(2x) f2x=2x2-12x+4 = 4x2-12x+4 = 4x2-12x+2 = 4x22x+2-12x+2 =…

Q: and f(a) f(x) = 4x² + 5x² + 6x-7 3 7 2. Find f(x), f"(0), given

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Q: Find the roots of the function f(x)=(2x-1)(x2+2x-3) with x belong to R

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Q: If you know that Q(x) is a quadratic function and that Q(5) = 10, Q(8) = 11 and Q(1) = 9 then: 1…

A: If you know that  is a quadratic function and that , then to evaluate the following integral.

Q: Solve the D. E. to the I. V. P. sinx(e-y + 1)x' – cosx = 1, y(0) = 0 %3D %3D (1 – e') (1 + cos.x) =…

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Q: Suppose f(x) = 2x² + 6x + 2. Compute the following: A.) f( – 3) + f(1) = B.) f( – 3) – f(1) =

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Q: Suppose f(x) = - 3x+5x + 6. Compute the following: %3D a) f( – 4) + f(2) = b) f( – 4) – f(2) =

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Q: 6. Simplify. a) (2x - 3x2- 6) + (6x – x³ + 4x² + 5) b) (x² – 4)(2x² + 5x - 2) c) -7x(x² + x - 1) –…

A: Given that -

Q: y = (2x+5) (x-4) y = (4x³- 5x)³ 11. y = 10. ƒ(x) = 2x-1 x+6

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Q: f(x)=4x' +2x°+lx² -9x° +7x +6

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Q: √(x³ + 2x² + x -5) e 2X dx

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Q: (c) 0$ y = cos (√√x² +1) (d) y 2x 2x +1

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Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.