Choose the rule that you would use to most efficiently find the derivative of the function. f(x) = Vx³ O Quotient Rule O Simple Power Rule O General Power Rule O Constant Rule

Q: 2² + y° = 1 = 2' - y %3| = z + y? = 1 +E z = I +y ² + y² + z² = 1 = 2° + y? circular cone sphere…

A:

Q: If f(x) = (3x² – 8) (5x + 4), find: f'(1) =

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: Let F = (5x,9x, 4) and G = (4,9x, 5). Calculate curl(F). (Give your answers using component form or…

A: The given functions are F=(5x,9x2,4) & G=(4,9x,5)

Q: Second Derivative Test. Consider the function f(x,y) = 4xy + 2ln(x) + 8y

A:

Q: Integrate f(x,y) =x+y over the curve C: x² + y = 81 in the first quadrant from (9,0) to (0,9). %3D…

A:

Q: Find an equation of the plane with the given characteristics. The plane passes through the points…

A:

Q: 1. In items a through c, do the following () Sketch the graph of the function; (ii) determine if fis…

A:

Q: integral all of this and show your solution: 1.  ꭍx^(-2)dx 2.  ꭍ√(x^2 ) dx 3.ꭍdx/xlnx

A: As per our guidelines we are supposed to answer only first three parts. Kindly repost others…

Q: Find the particular solution: y" + 16y' = 0, when x = 0, y = 0, y' = 0, y" = 1

A:

Q: Evaluate the definite integral. 7t ej+t O e? - 1 i - elj+ 7 2 O e? - 1 i+ 7 k - O eľ - 1 i - 7 1 k -…

A:

Q: 1. Consider the graph of the function f(x) = 1.a. Is the function f (x) continuous at x = 1? Justify…

A: We need to find if the function is continuous or not in given interval.

Q: Question A vertical cylinder is leaking water at a rate of 5 m /sec. If the cylinder has a height of…

A:

Q: An integral is given that can be evaluated using integration by parts. Write expressions for u, du,…

A:

Q: Evaluate the integral by first modifying the form of the integrand and then making an appropriate…

A:

Q: (24a²x + 8ay?)i + (82³ – 2ay)j – (2z + 8x² + 8y?)k. (a) Find the value(s) of a making div F = 0 a =…

A:

Q: Find the absolute extrema of the function on the closed interval. g(x) = 9 sec x, 3 minimum (x, y) =…

A:

Q: 里() t² + 5 1 lim t一+05t2 +6'2t (?, ?)

A:

Q: Given the power series Σ 2 n A, x" n = 1 Use the technique that we covered in this lesson to force…

A:

Q: Describe the graph of the equation. r = -9i+ tj + (r² – 1) k O It is a parabola in the x = –9 plane,…

A:

Q: (a) Find the numbers at which the following function y =f (x) is discontinuous. And at which of…

A: We have to find the continuity and discontinuity points. According to our guidelines we can solve…

Q: Choose which of the following is the EXACT value for the area bounded by y = e" and y = -e' on the…

A: The region is bounded by y=ex and y=-e-x on the interval 1≤x≤2

Q: Complete the table by identifying u and du for the integral. dx u = g(x) du = g'(x) dx u = du = dx

A:

Q: 5. St V1-t dt

A: We solve this integration by substitution method by putting                         1 - t3 = u…

Q: dy 2, find dt da when I = 1 dt x and y are functions of a third variable t. If V + /T 4 and |3D %3D

A:

Q: Find the angle 0 (where 0° < 0 < 180°) between the following vectors. Give your answer accurate to…

A:

Q: y" + (x - 3)y' = 0 Plug in the appropriate power series for "y" and "y'" in order to convert the…

A:

Q: Let C = (1,–3, 2) and D = (-1, 2, – 3, ). Find the following. (a) The cosine of the angle between D…

A:

Q: fx,у) %3D -2у + зху + 8у - 4х2- бх — 7 then f equals ху О Зу - 8х — 6 O -12y O Does Not Exist Оз…

A:

Q: Question Consider the function f(x) = 2 tan (x) – 3 over the interval Does the extreme value theorem…

A: Given function f(x)=2 tanx -3     ;  -π3 , π3

Q: 1/4+1/5-1/6+1/7-1/8

A: Given, -1/4+1/5-1/6+1/7-1/8

Q: Find the general solution of the given linear differential equation. y'''' − 2y''' + 5y'' = 0

A:

Q: Vtan(7x) sec?(7x) dx

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

Q: In evaluating a double integral over a region D, a sum of iterated integrals was obtained as…

A:

Q: 3. Is the function f(x) = csc2 + sec x- cosr even, odd, or neither? Show algebraically. %3D 4. Write…

A:

Q: Write the following complex number in trigonometric form: - 2 + 2i

A: I am going to solve the given problem by using some simple calculus to get the required result of…

Q: You are given a sphere of radius 2. A hole of radius b (b < 2) is drilled through the center of the…

A: Follow the procedure given below.

Q: dy: cos(y) + 7 Consider the integral This can be transformed into a basic integral by letting u =…

A: We can fill up the blanks as below.

Q: ピ+5 1 lim t一+0|5t2 +6'2t (?, ?)

A:

Q: Suppose a person travels at a rate of 4 ft/hr toward the foot of a street lamp pole 51 ft high. The…

A: Solution: Let  H denotes the head of the person and P denote the top of the pole.  At any instant…

Q: 3x2 — 9х + 11 2х + 4

A: Given query is to find the derivative.

Q: Flight of a Model Rocket The height (in feet) attained by a rocket t sec into flight is given by the…

A:

Q: Domain. The domain of 8/x + 8 g(x)=. 3x2 - 12x + 9 can be written: O (-0,3) U (3,8) U (8,00) O…

A: The given function is: gx=8x+83x2-12x+9 To find the domain of the function g(x).

Q: If a = - 5i – 3k and b = i+ 2j then: - 2a – 3b i+ j+ k

A:

Q: 5 x - 2 Horizontal Asymptotes. Find the horizontal asymptote of f(x) = 4 x2+5 x-2 O y = 0 There is…

A: The given function is: To find the horizontal asymptote.

Q: 4. y = Vesinx + 2

A:

Q: 15 dx +C + x2

A:

Q: n(3n – 1) - 1+4+7+...+ (3n – 2) =

A:

Q: 11. y'+3y = 3x2e-3x %3D

A:

Q: 25. A hemisphere has a radius of 3 cm. Draw complete with labels the cross section with equation of…

A: the derivation of moment of inertia is given as follow but mass is misssing.

Q: given f (x) = 3/5 cos (6x), what is the largest possible value for f (x)?

A: Given query is to find the largest possible value of the function.