Suppose that f(x) = 3√x. 1. What is the average rate of change of f(x) over the interval [1,4] ? none 2. What is the (instantaneous) rate of change of f(x) when x = 1 ?

Q: At a sand and gravel plant, sand is falling off a conveyor and onto a conical pile at a rate of 14…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: A certain bacterial culture grows at a rate proportional to the number of bacteria present. If the…

A:

Q: Find the average cost function if cost and revenue are given by C(x) = 168 +5.4x and R(x) = 8x…

A:

Q: A can of soda is placed inside the refrigerator. The soda has an initial temperature of T = 70-F.…

A:

Q: 2. Find the distance between P₁ - and P₂ (-1).

A:

Q: Given: g(x) = f(x) cot(x) + kx, where k is a real number. f is differentiable for all x; f(π/4) = 6;…

A:

Q: Your monthly profit (in dollars) from selling magazines is given by P = 2x + √x where x is the…

A: Your monthly profit in dollars from selling magazines is given by p=2x+xwhere x is the number of…

Q: Question The position of an object moving along a straight I after t seconds is modeled by the…

A:

Q: Evaluate x/4 0 x/4 S 3√/1+ cos 4x dx. 0 3√/1+ cos 4x dx =

A: To evaluate the integral

Q: Suppose that f6x² cos(x³) sec² (sin æ³) tan(sin æ³) esec² (sin z³) dx = G(x) + C = F(x). Determine…

A: The given integral is; 6x2cos(x3)sec2(sinx3)tan(sinx3)esec^2(sinx^3)dx=G(x)+C=F(x).

Q: The cross product (u x v) of the two vectors u = i-2j + k and v = 3i + j - 2k is -3i - 5j7k. True

A:

Q: A business has found that it can sell 660 items if it sets its price to $63.02. However, if it…

A: let x be number of items sells and p be price of function

Q: A can of soda is placed inside the refrigerator. The soda has an initial temperature of T = 70-F.…

A: Given differential equation dTdt=kT-40 Lets solve it using separation of variables.

Q: Suppose that the piecewise define function f is defined by f(x) = Select the correct answer below:…

A:

Q: Help Entering Answers .Write the equation z = √² + y² in spherical coordinates. (Simplify as much as…

A:

Q: Find the solution of the differential equation (1 + y²)dx + (1 + x²)dy = 0

A:

Q: The negative real solution to the equation is a = Number 2-9-1=0

A: The given equation ex2-9-1=0 We have to find the negative real solution.

Q: 1. Discuss the monotonicity (i.e. identify the intervals of x over which the function is increasing…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: Consider the function g whose graph is given below. -6 -5 3 H -1 -2 -3 6 (a) Determine if g is…

A: Answer Think about the function 1x on the open interval (0,1) - it is not defined at 0, but this…

Q: -1). 3. What is the locus of the P(x, y) that is equidistant from (2.3) and (7,-3).

A: Coordinates are ( 2 , 3 ) and ( 7 , -3 )

Q: An airplane flies at an altitude of y = 4 miles toward a point directly over an observer (see…

A:

Q: The graph of f(x) is shown below. Which of the following statements are true? 00 7 6 5 4 3 2+ H -5 Y…

A:

Q: Find f'(t) if f(t) = − 5t² + 6t + 1.

A:

Q: Determine whether the lines - L₁ :ŕ(t) = ( − 1, 0, − 2)t + (2, − 2, 4) and L2: p(s) = (3, 0, 6)s +…

A:

Q: Find the indicated derivative. q²+2 3q 2 dq 11 dp dq for p =

A:

Q: Question Suppose that the piecewise define function f is defined by f(x) = Determine which of the…

A:

Q: 2 Y = x ²² - K² K is a constant X² + K² K is

A: Topic- derivative of a function we are given y=x2-k2x2+k2and we know thatddxuv=vu'-uv'v2ddxxn=nxn-1

Q: If 6x²y + xy² = 7x, find y' by implicit differentiation. y' =

A: Solution is done in step 2

Q: Use logarithm properties to expand the expression log5 O a.) log5 (25x³-y²) O b.) 2+3log5x+7log5y O…

A: Given , log525x3y7

Q: (ln(x))³ x de is u =

A:

Q: Solve the differential equations. 1. X 3

A:

Q: If x¹ + x²y + 7y² = 14, find y' by implicit differentiation. 2

A:

Q: 3. Find the derivative of f(x) = cos¹ (3x²)

A: Solve 3

Q: Find an expression for the inverse of f(x) = e³x+1. f-¹(x) = 4

A: Topic- functions and inverse functions We are given, f(x)=e3x+1 we know that ln(ex)=x

Q: 1. For each of the following functions, determine if it is best described as a product, a quotient,…

A: The objective of the question is determine the given function as product or quotient.

Q: Suppose that a population of dog breeds cannot exceed 1,000. The growth rate is 0.4 per year. How…

A:

Q: For f(x)= x2+4 and g(x)=x2-4 find the following function (fog)(2)

A: Given, f(x)=x2+4g(x)=x2-4

Q: Find the equations of the tangent lines to the curve y= x^2-2x at its points of intersection with…

A:

Q: (A) h(x)=2f(x) h′(2)=     (B)  h(x)=−5g(x) h′(2)=   (C)  h(x)=6f(x)+3g(x) h′(2)=   (D)

A: Let's solve. function given as a relation of other Function.

Q: Suppose the revenue from producing and selling a units of a product is given by R(x) = 3x – 0.01x²…

A:

Q: I thought the Area of Sector is  A = 1/2 r^2 theta Is this the same formula or different formula?

A:

Q: Given the piece-wise defined function: 8 x < 0 f(x) = { 16 x ≥ 0 f(0) = Calculate the following…

A:

Q: A population P exhibits logistic growth according to dP P the model = 0.05P|1- where the initial dt…

A: Solution

Q: Find the limit. 41) lim X-8 (√7x² +10-√√7x²-3)

A: This is a problem related to limit. Please follow the procedure given below..

Q: Find the speed at the given value of t: r(t) = (et-5, 12,5t-¹), t = 5 v(5) =

A:

Q: Solve the given differential equation 5x4cos 2 ydx - dy = 0 (A) y = tan-¹ (x5 + C) B) y=x5+ C C y =…

A:

Q: By cutting away an x-by-x square from each corner of a rectangular piece of cardboard and folding up…

A: Since, it is given that by cutting away an x-by-x square from each cornerof a rectangular piece of…

Q: A population P exhibits logistic growth according to dP 05P(1-7/15) the model = 0.05P 1 dt…

A: To find the value of X.

Q: (a) Find the closed area determined by the graphs of x = 2 - y² and y = x by following the y axis…

A: givenx=2-y2  and y=x

Q: 1.) dy dx + y = cos(x) = 0

A: Let's solve given differential equation.