1) *A calculator is required for this question 4 (2, 4) 3 R (0, 2) 2 1 -1 1 2 R and S be the regions bounded by the functions f(x) = 1+x + e**-2x 8(x) — х4 — 6.5х? + бх + 2. and (a) Set up an expression involving integrals that calculates R+ S, then solve using a calculator. (b) Let R be the base of a solid whose cross sections perpendicular to the x-axis are isosceles right triangles, with one leg on R. Set up an integral that calculates the volume of this solid. (c) Set up an integral that calculates the volume of the solid generated when R is revolved about the line y = 4

Q: In the region in the first quadrant bounded by f(x) = 4x - x2 and the x-axis, what are the lower &…

A:

Q: Question -2x2 + 4x dx J (x² + 1)(x² – x)

A: Given: ∫-2x2+4xx2+1x2-xdx

Q: Determine the quotient and remainder if P(x)=x'+6x'+2x'+x-3 is divided by D(x)—x'—2х—1

A: Topic = Algebra

Q: (a) h(x) = x^√√x² +1 (b) f(x) = (3x² - 2x+1)³(x¹ -2r²- 3)² 4 (c) g(x) = (3-4) ¹ 5x+7

A:

Q: 1. if f(x)= x2-4,  g(x)=x3 , F(x)=1/(x-3) a. F(g(y)) b. f(square root of x4+2)

A: F(g(y)) can be obtained by replacing x by g(y) in F(x)

Q: Prove that for integers y=1 the equation 3h-n (2x₁ + x₂ + 4x₂) +3² (~1(2x₁+x₂+.+xn-1)+...+3^-1 (2²₁)…

A: We will use contradiction to prove it.

Q: 3x10 + 3a5 + 5æ² + 7. What particular solution that satisfies Suppose f'(x) 455 -? 66 f(1)

A:

Q: Consider the following quadratic f(x) = x² – 7x + 3 with the roots a and ß. %3D Suppose the new…

A:

Q: Bonus: Expand into standard form, use the LONG THREE BOX METHOD to produce f'(x), and then find the…

A:

Q: Find a formula for f-'(x) and (f -1)'(x) if f(x) = V х-2

A:

Q: (In 2z - 1) – 25z(In Given the function f(z) = f t In t – tdt then by using the fundamental theorem…

A: Given problem:-

Q: The graph of g(x) is shown below. The image includes two straight lines and a semi-circle. Use this…

A:

Q: If f(x) = g(h(3x)), then f'(x) is equal to which of the following? Og'(h '(3x)) Og'(h(3x))h (3x)-3…

A:

Q: Please help (41-45)

A: Here we have to find the derivative.

Q: Solve for a) given y= 2f(x) solve for x b) given y=-3f(2x) solve for x c) given y= f^-1 (4x) solve…

A: Given Functions are as follows

Q: 2+(-6₁-16) m=(-10) - 1 (-6)-4 m= - 17 pl: (417) pt = (4₁7) S y moc + b 7 = -12 (4) + b (1= -68 = +…

A: Given:The graph of a line joining two points:  and The aim is to find the general form of the line…

Q: x +5 Given the function g (x) find g' (x) x² +6x O 8' (x) = x* +6x³ +5x² +30x x² (x+6)? O 8' (x) 2x3…

A: Given, gx=x2+5x2+6xDifferentiate…

Q: Suppose that f(x) r'(x) = 4²x+5]n(4) - s+2 + 5x Find f'(x). #

A:

Q: E (3x(9 ^ b) V Jaæ(p ^ 0)) = 3x(p A (4 V 0))

A: To prove ⊢(∃x(φ∧ψ)∨∃x(φ∧θ))≡∃x(φ∧(ψ∨θ)) Here we have to use existential quantifiers i.e. notation of…

Q: c. If you own a company that sells shoes and your marginal revenue (in Ringgit Malaysia) from the…

A: Given Marginal revenue from the sale of x shoes is given by, R'x=Axx2+26191-23 Here A is an integer…

Q: SOLVE BY LINEAR METHOD - y'- 3 X Y = x 3 cos (x)

A:

Q: 8. Find all the roots of f(x) =x* - 4x' + 6x² – 4x+5 if 2-iis one root.

A: Topic- roots of polynomial

Q: x'-x+2 If fx) =ア+7 6. , find f'(x). (5x-1) (A) (3x) (x'+7)(5x-1)-(x'-x+2)(3x) (x+7) (B)…

A: Given query is to find the derivative of the expression.

Q: 8. Find all the roots of f(x) = x' - 4x' +6x² – 4x+5 if 2– i is one root.

A: We will find all the remaining roots as following.

Q: 22. Find f/(x) and simplify 1 -1 a) f(z) 3-52+1 3 b) f(x) 1.8Vc) f(x) = 32

A: Given, functions

Q: 4. Let 0 ‡ b, c E Rn and define A = be E Rnxn. Show that (a) R(A) = span{b}, (b) N(A) = {x ≤ R" |…

A: (a) We are given that A = bcT                    where, c ∈ Rn     So, R(A) = { Ax : x ∈ Rn×1 }…

Q: Use Midpoint Rule, the distance travelled during this period is, M, =| v(x, )+ v(x, )+ v(x, ) + v(x,…

A: Definition used – The value of the function at a point – The value of the function at a point can…

Q: If f(4) = 3 and f'(x) 2 3 for 4 s xs 9, how small can f(9) possibly be? (9) 2

A:

Q: 2x² + 3 Find f'(x) given that f(x)= x² - 5x+2 5) Find f'(x) given that f(x) = (2x³ + 2x² − 3)(3x³ -…

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

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.