1. What is the area of the region enclosed by the functions f(x) = 1+2x - 3x2 and g(x) = -x- 5? 10 12 13 n (A); (B) (c) (E) rat)-1+2 -3 x (D) 一2

Q: |x + 7| X < -7 X + 7.

A:

Q: 1.2 Find the domain and range for f(x) = √4 − 2x + 5

A: f(x)=4−2x+5

Q: 20. Evaluate f(a+2) for ƒ(x) = %3D 4x-8*

A: Given: f(x)=34x-8

Q: (b) Write z = (3- 3i)+ in the form of x +iy.

A:

Q: 3. 1 x2+12x-5 (x+1)(x-7) dx

A: We need to solve the following integral I = ∫x2+12x-5x+12x-7dx…

Q: 4 Compute f(g(x)) where f(x) =x* -x and g(x) =x²-11. dx The answer is

A:

Q: What is the value of x at which f(x) = -5x2+4x+17 has an extremum?

A: We have to find for what value of x it gives extremum

Q: 3 7) Evaluate: f(-x² + 4x − 1)dx 1

A: Given, ∫13(-x2+4x-1)dx

Q: 8) Find 4 given : f(x)=- (3x² – 2x +1)'

A:

Q: Suppose a car drives north on I-95 starting from Miami. Let f(t) denote thenumber of miles from…

A: f(5) − f(3)/5 − 3 represent displacemennt/time taken from 3hours to 5 hours i.e. 2 hours

Q: 4 If f(x) = ln(2x² – 3) then f'(x) =? - 2x a) 2x2 – 3 - 4x b) 2x2 – 3 2x c) 2x2 + 3 -4x 2x2 – 3 -…

A: f(x) = ln(2x² - 3) So, f'(x) = 1/(2x²-3) × (2x²-3)' So, f'(x) = 4x/(2x² - 3) .... Option (b)

Q: If f(x) = x*3 − 6/x, find the following:a) f(-1/2)b) f(2)c) f(-2)

A: Answer: a) -27/2 or -13.5

Q: Evaluate the difference quotient fla +h) – fla) for the function Ar)= 4х-3 (h - 6)/9h 1/9 4/9

A:

Q: 1. Write the following in the form f(x) = Ba". - (;) (*) 20 (a) f(x) = (b) f(x) = 5(3")(9ª) (c) f(x)…

A:

Q: 1b. please express in the notation p(x)=d(x)q(x)+r(x)

A: Given that,   Where p(x) denotes a polynomial and d(x) denotes a divisor.   Q(x) is quotients and…

Q: 5. How many zeros does this function has f(x)= 2x? - 5x - 7? с. 1 d. 3 a. None b. 2

A:

Q: Evaluate the difference quotient for 7x+1. Az) - f(x) = 2 7/2 7 O 1/2 O O

A: Here we have to find the quotient difference of a function.

Q: 7. Given f (x) = 4 +3|2x + 4|, find f (-3). %3D

A: Given that f(x) = 4 + 3 |2x + 4| We need to find value of f(-3). Now, Put the value x = -3 in given…

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.