8. What rule should be used in deriving f(x) = x³? A. Constant rule B. Sum rule 9. Find dy/dx y=e³x A. e³x B. 3e³x 10. What is the derivative of -cos(x)? B. -sin(x) A. sin(x) C. Power rule D. Difference rule C. 3x C. cos(x) D. 3x³x D. -cos(x

Q: %VIII. १:०. By using the differential operator D and it's inverse, solve this equation: y"+y=sin(x)…

A: The given equation is;  y''+y'=sinx.

Q: Q5) Evaluate the following integral by using Partial Fractions Method 2x²-3x+2 y = √ ₁²₂²³² Sa dx…

A: Given problem:-

Q: 6. Find the derivative of y= 2x² (3x-4). A. 6x³ - 8x² B. 18x² - 16x C. 15x² - 6x D. 6x-4

A:

Q: calculusssss please

A:

Q: Determine whether the statement is true or false. If it is true, explain why it is true. If it is…

A: Here we have to choose the correct option.

Q: Use the Lagrangian method to minimize f(x, y, z) = x² + 2y² + z² s.t. x² + 2y + 3z = 8 Find the…

A:

Q: Given the function f(x) = 3x - 2, find and simplify the following values: f(a) = f(a+h) = =…

A: Given,  f(x)=3x-2

Q: Consider the function below. ex f(x): 8 + ex (a) Find the vertical asymptote(s). (Enter your answers…

A:

Q: 18 [™ f(z)dz where a = 11 - F f(x)dr = [² (² and b 0 f(x)dr

A:

Q: A radioactive substance decays in such a way that the amount left after t years is given by A=100e…

A: Follow the procedure given below.

Q: 6. The diagram below shows a regular hexagon. For each vector expression, write a single vector that…

A:

Q: 4. At x = 4, the function f(x) = (x², x ≤ 4 (4x, x>4 A. continuous but not differentiable B.…

A:

Q: Q2: Fill the blank: 1) lim (1+)52 x48 4x 2) lim x.e-3x = X-80 3) (csch¯¹x³) = . dx 5x =...

A:

Q: 4. Find an equation for the plane through (1, 3, 4), with normal vector .

A: topic- equation of plane with point and normal vector

Q: 33. " +9y sin 2x; y(0) = 1, y' (0) = 0 34. y" + y = cos x; y (0) = 1, y'(0) = -1 35. y" - 2y + 2y =…

A: Given: y(3)-2y''+y'=1+xexAuxilliary equation: m3-2m2+m=0Therefore, m=0,1,1Complimentary…

Q: 1 2. Find the length of arc of the curve x = + from the point where y = 1 to the point where y = 2.…

A:

Q: Given f(x) = = Domain: 1 x + 2 and g(x) = 6 X - 4' find the domain of f(g(x))

A: We have to find the domain

Q: Evaluate the following integral. 1 tan (√3x) 1 2 (3x)² +(3x)² - 13 0 MIN 3 dx

A: Here we have to find the integral

Q: k 4 · 3k+1 50

A:

Q: x Q3: Show that csch-¹ (²7) = coth-¹(x+¹) x-1,

A:

Q: QUESTION 12 Which method of apportionment always satisfies the quota condition? OA. Hill-Huntington…

A: Topic = Algebra Correct option = C

Q: 4. For the relation explain the transformations, y-intercept, asymptote, domain/range, show at least…

A: The given function is y=2-x+2-1 ............................................. (1)

Q: Below is the graph of y=e*. Transform it to make the graph of y=-e* +5. Give the domain and range of…

A: Given problem:- Graph of y = ex   Transform it to make the graph of y = - ex + 5   Give the domain…

Q: %VIII. १:०. By using the unlimited coefficients method, choose the correct answer for this equation…

A:

Q: A projectile is launched straight up in the air. Its height (in feet) t seconds after launch is…

A: topic- average value of function over interval

Q: Find indicated Partial derivatives u= √√√√² +5² 2 S r = y + x cost, S = x + y sint d² u dxy

A:

Q: 4) Find the intervals where the following function is concave down: ππι y = 2sin² (2x) - 4x, x € -

A:

Q: 1. The effectiveness of studying for an exam depends on how many hours a student studies. For a…

A:

Q: If c = 192, ZA = 79° and LB = 55°, b ; Assume ZA is opposite side a, LB is opposite side b, and ZC…

A: answer is in next step. please give a like !!

Q: Find (dy/dx) for: tan-¹(x² + y) - eln(x³y) = 5sinh(y)

A:

Q: 1. If x=11, 23and |-= 30; calculate +

A:

Q: Find dy /dx for the following functions: -) y².cotx= [sin(x. y)]-¹ b) y = (lnx+x) tan x

A:

Q: Evaluate x³ + €

A: On solving this we will get

Q: If y = √1 − x² sin¯¹x, prove that (1− x²) ¹ + xy = 1− x². dx

A: We can prove the given the result by differentiating the given function.

Q: ) Find (dy/dx) for: tan-¹(x² + y) - eln(x³y) = 5sinh(y)

A: We need to find dy/dx.

Q: ) Find (dy/dx) for: tan-¹(x² + y) - eln(x³y) = 5sinh(y)

A:

Q: H.w2: evaluate 0.5 0.5 sinxy dx dy, using the Ax=Ay = 0.25 0 1+xy

A:

Q: Find the general solution to: y(x² +1) + y' = 0, for y > 0.

A:

Q: Find the area of the region between f(x) = x² + 2 and g(x)= x - 1 on the interval [-2,2]

A: The functions are f(x)=x2+2  &  g(x)=x-1

Q: dy 1. Determine for each of the following. Do not factor but simplify where appropriate. dx a) y =…

A:

Q: 1. So letet Jo 1+ e* t -dx

A: The given integral,        ∫01ex1+exdx

Q: (x² - 12x + 9) dx (x²-3x + 2)²

A:

Q: Find indicated partial derivatives: дz a) yz = ln(x+z)

A: We have to find partial derivative of given function.

Q: 20. Which of the following is a direction vector for the plane with Cartesian equation 3x-2y-52+3-07…

A: Given problems:- 20. Which of the following is a direction vector for the plane with Cartesian…

Q: Use the Table of Integrals to evaluate the integral. Show ALL work. S 11x³√4x²x¹ dx

A: Follow the procedure given below.

Q: ) Prove that sech¯¹(x) = In ( ¹+ √¹-x²) X

A:

Q: Q5) Evaluate the following integral by using Partial Fractions Method 2x²-3x+2 y = S dx (x - 1)². (x…

A:

Q: Q2) Use the chain rule to express dy /dx in terms of x and y y = sint and t = cos x where t = 0

A:

Q: 3. (3y² + xcos xy) + (3x² + ycos xy) = 0 dx a) y + sen xy + x³ = 0 y² + sen xy + x³ = 0 y² + sen y +…

A:

Q: Determine the value of f(-3) for the function f(x) 00 O Undefined 3 B O 15 O x³ +18x²+104x + 192 for…

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