Evaluate the following integrals: Show CLEAN AND CLEAR solutions also indicate what rules/formulas you used to obtain your answer. 3. SVt + 2t3 + t?dt

Q: 4. For the functions f (x) = x + 2 and g(x) = x² – 2x + 7, which expression has the greatest value?…

A:

Q: The plane a+ y-0 intersects the surface 7+ 2:21 along a curve C. Use Lagrange multipliers to find…

A: We have 2 surfaces intersects to form a curve. We need to find the maximum and minimum of a function…

Q: 2. Refrigeration slows down the growth of bacteria in food. The number of bacteria in certain food…

A: Given number of bacteria in a certain food is approximated by BT=15T2--70T+600 where T represents…

Q: Given that f(x) 2x+7 %3D 3x-5' determine the equation of f-(x)

A: The given function is fx=2x+73x-5. Let fx=y. y=2x+73x-5 Replace x and y as follows. x=2y+73y-5

Q: 3. Ever wondered what trigonometry is good for? Describe a potential career choice that you can…

A: Trigonometry has various applications in engineering, oceanography, astrology, space science, flight…

Q: At the point P(1,2, 3), a function f(z, y, z) has directional derivative of-4 in the direction…

A: We have to find the value of fy(P).

Q: 1. A spherical balloon is being inflated. The radius, r, of the balloon is 0 cm initially, and is…

A: A spherical  ballon  is  being inflatedAt   t=0   radius of sphere r=0     a  Volume    vr=43π r3…

Q: Q3/ Evaluate the following integral and simplify it into the final form: x-6x-2x-3x+4 x'+2x+3

A:

Q: 5. If f (x) = Vx, g(x) = x + 5 and h(x) = x² – ÷, 1 find the following.

A: Given,            fx=x , gx=x+5  and  hx=x2-1x .

Q: Find a value of b > 0 that makes

A: Improper integral is a definite integral with either the lower limit as infinite, the upper limit as…

Q: 10.Given f (x) = 9x² + 7x and g(x) = 2 – x. Determine 5g(x) – f(x) a) 9x2 + 6х + 2 b) —9х2 — 12х +…

A: Given Information -  f(x) = 9x2+7xg(x) = 2-x We have to find the value of 5g(x) - f(x).

Q: 1. A pilot must fly 23.0 km before she is over the ocean. The angle of depression to the ocean…

A: From the given information. The distance in which the pilot must fly is 23 km. The angle of…

Q: 2 Skill Check Use the quadratic formula to solve the equation. 2- 4x + 3 = 0 x² +x - 1 = 0 2r2 + 3x…

A:

Q: 2. Given f(x) = –vx + 2 and g(x) = x² – 2x + 7. What is the domain of q (x) = f(x) – g(x)? a. Can't…

A: Topic- function domain

Q: 3x |2y 4y (5х — 20)

A:

Q: In the context of global alignment (scores: match = 6, mismatch = -2, and gap = -2), what will be…

A: Solution Given

Q: Today is January 1st, 2022. Cat is a loan shark, and she offers you the following deal. She will…

A: Given, For the loan Principal = P Time period = 12 months We have to find the which scheme we choose…

Q: 7. Given the functions f(x) = x³ - 81x and g(x) = x + 9, determine the simplified equation for the…

A: we have given the two real valued function f(x) , g(x) of polynomial form and we need ton find…

Q: 12. If f(x) is a non-constant linear fucntion and g(x) is a quadratic function, then what type of…

A: f(x) is linear function so f(x) can be expressed as  f(x)=ax+b, where a≠0 and b are constants. g(x)…

Q: 1. Given h(x) = 5x² – 3x – 2 which pair of the equations below are possible - equations for f(x)and…

A: we need to find the subtraction of two real valued polynomials.

Q: 2. If f(x) = 2x – 1 and p(x) = = cos (x). Find x, for 0 < x < 2n, if (f •p)(x) = -2

A:

Q: 8. Use the graph given below to answer the questions. y 6- 4 g(x) a) Find f(g(1)) b) Find (f •…

A:

Q: A $1000 investment earns interest at a rate of 4.2% per annum, compounded monthly. Another…

A:

Q: Integrate X dx 1+ x²

A: Given, I=∫x51+x12dxOrI=∫x51+x62dx

Q: A roof has the shape of a scalene triangle. On one side of the roof, the angle of inclination is 43°…

A: given triangle is