a) Find the derivative using the definition of derivative: X 1 2 7 f(x) f'(x) 1 = ! b) State the domain of f(x): c) State the domain of f'(x): ९

Q: Find the average rate of change of the function f(x) = x² + 9x from x₁ =2 to x₂ = 5. The average…

A: As we know that; The average rate of change of the function fx between the interval x1≤x≤x2 is given…

Q: 6. g(x) = sec (3x²)

A: We can solve it by chain rule dy/dx = dy/du * du/dx

Q: Problem 1: Using differentials, approximate the change, in terms of 7, in the total surface area of…

A: Radius of cylinder r= 3units  Altitude of cylinder h= 5units  dr/dt=0.2 unit , dh/dt =-0.1 unit…

Q: 4x²-x-2 dx (x+1)(y+1) 3. x2 dy ; y(1) = 1

A: To find out the solution of the differential equation.

Q: The population of the world x years after the year 2010 is predicted to be 6.9e0.00743x billion…

A: NOTE: Refresh your page if you can't see any equations. . the population(in billion of people) is…

Q: Problem 3: Determine the two-variable function F(x, y) if Fy(x, y) = y sin(πxy) - x given that F(x ²…

A:

Q: 1. Evaluate the following integral Si -10 2t²cost 8(t-n) dt

A:

Q: · γ΄ = 4x2+y2 χν

A:

Q: Solve the following quadratic equations using elimination method: Question 7: x2 - 4 - y = 0 x2 - 4…

A: Given, y= x^2 - 4 equation no.(1) & y= x^2 - 4 equation no.(2) Now, using elimination method.…

Q: - y" - 3y'- 4y = 5 ex ANS. y = (c₁ + x)e²x + c₂e¯x.

A:

Q: Determine the two-variable function F(x, y) if Fy (x, y) = y sin(xy) + x given that x^2 + πχ2 F(x₁ -…

A:

Q: Problem: A tank contains 20 kg of salt dissolved in 5000 L of water. Brine that contains 0.03 kg of…

A:

Q: 5) Use the fact that 6i is a zero of f(x)=x³-2x²+36x-72 to find the remaining zeros.

A:

Q: 17. [x — y arctan(y/x)]dx +x arctan(y/x)dy =0.

A:

Q: Find the cross product a x b. a =j+9k, b = 5i - j + 2k

A:

Q: A loan shark lends you $90 at 2% compound interest per week (this is a weekly, not an annual rate).…

A:

Q: g(x) = 2x-3 at x = 3

A: Given g(x)=x2x-3 at x=3Subtitute x=3 in g(x)

Q: x² + y² = 8 y = x + 4

A: Solution

Q: 56. s 1 √x² +9 dx

A: See this solution in below.

Q: Eliminate

A:

Q: Problem 3: Determine the two-variable function F(x, y) if F₂(x, y) = xexy + y given that F(-1½ ‚Y) =…

A: Please see the below picture for detailed solution.

Q: Atmospheric pressure P in pounds per square inch is represented by the formula P = 14.7e-0.21x,…

A: To find out the peak of mountain for the given atmospheric pressure.

Q: Let f be a differentiable function such that f (3) = 4 and f' (3) = 5. If g(x) = x² f (x), what is…

A:

Q: Find two unit vectors orthogonal to a = (2, 1, 3) and b = = (-1,0,-5) Enter your answer so that the…

A: Given vector a = ⟨2, 1, 3⟩ and vector b = ⟨-1, 0, -5⟩  *** Vectors orthogonal to vector a and vector…

Q: Solve the System. Give answer as (x, y, 2 -x-5y4z = 14 2x + 5y-6z = 9 4x + 5y + 6z = -21

A:

Q: If the tangent line to y = f(x) at (7, 3) passes through the point (0, 2), find f(7) and f'(7). f(7)…

A: Given: The tangent line to y=fx at 7,3 passes through the point 0,2 We have to find the value of f7…

Q: 2x dy - y dx = x²y² dx

A:

Q: 3. Determine whether the following function y = c₂x + c₂x³ + 2x²e² is a solution to the differential…

A:

Q: 2) Find the surface area obtained by rotating y = √t. t € [4.9] about the t-axis.

A:

Q: Solve the following differential equation. 2. 2xy dx +(1+x²)dy=0

A:

Q: Let P be a point on the parabola y = 4x2, and let Q be the point where the perpendicular bisector of…

A:

Q: Let f(x) = 3x² -6x+7. You must show all your algebra. is worth zero points. a) Find the axis of…

A:

Q: A rectangular piece of cardboard measuring 8 in by 10 in is to be made into a box by cutting equal…

A:

Q: 2. Evaluate the following and give the exact value: Show your complete solution. cos y [*1/2 [ ***…

A: The given integral is Sin(y+z), z from y to pi -y, x from 0 to cosy, y from pi/6 to pi/2. Repost the…

Q: 1. Using differentials, solve for the approximate change in the hypotenuse of a right triangle if…

A:

Q: 3. Let C be the curve given by {(x, y) = R² | 2³ + 2x² + xy³ = y³}. Find the r-coordinates of the…

A:

Q: [x) = √x. (a) Simplify f(22 + h) − f(22) - h Algebraically simplify your answer until you have…

A: Given query is to find derivative using definition and then equation of the tangent.

Q: 3. Determine whether the following function y = ₁x + ₂x³ + 2x²e* - 2xe* A is a solution to the…

A:

Q: Consider the following sequence: (an) = = {n-n²} Use an+1-a, to show that the given sequence (a) is…

A: Given :

Q: 1 lim [ y→0 Lln (1+y) |- 1 sin y.

A: Given: limy→01ln(1+y)-1sin y

Q: Create 3 exact differential equations and solve for their test for exactness and general solution.…

A: We create 3 exact differential equations and solve for their test for exactness and general…

Q: Find the average rate of change of the function ƒ (x) = x³ + 1 on the interval [-1,3]

A: The function is given by fx = x3+1 To evaluate: The average rate of change of the function fx on the…

Q: . Use congruences to show that there is no solution to x³ + x² − x + 1 = 1522745.

A:

Q: 8) Is f(x) = 6x² - odd, even or neither? You must show all of your algebra. x

A: To verify that function is odd, even or neither.

Q: 2. Evaluate the following and give the exact value: π/2 cos y are the (sin(y + 7) dz [** dx dy

A:

Q: 8. y" 3y'- 4y = 5 ex. ANS. y (C₁ + x) e²x + c₂e-x.

A: The given differential equation is; y''-3y'-4y=5e4x.

Q: The monthly cost of driving a car depends on the number of miles driven. Lynn found that in May it…

A:

Q: Find a differential equation whose general solution is 8t y = C₁est + c₂e-4t. = 0

A:

Q: π/2 cos(y) 1/6 So π/6 -y ㅠ y sin (y+z)dz dx dy

A:

Q: Let f(x)=4x 2+12x−2 Using the definition of derivative, f'(x)=limh→0 f(x+h)−f(x) /h, enter the…

A: