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Q: Consider the function f(x) = x2 + x and the point (1, 2). (a) Find the slope of the tangent to the g...

A: To determine:Part a) The slope of the tangent to the function f(x) at any point.Part b) Slope of tan...

Q: Find dy/dt when x=4 and dx/dt=-3, given that x^3+y^3=72

A: First obtain the derivative of the given equation as follows.

Q: Find the slope, x intercepts and y intercepts for the following  y= 3x-24  x/2-6=3y 4x-3y=24 y=4

A: Compare the given equations with the standard equation of line, y=mx+c where m=slope of the line

Q: Calculus Question

A: Consider the given function.

Q: Kirk’s average driving speed is 7 kilometers per hour faster than Thor’s. In the same length of time...

A: Let the Thor’s speed be x, then the speed of Kirk’s speed is x + 7.The distance which covered by Tho...

Q: Calculus Question

A: According to the given information the average surcharge for non-account holders who use ATM can be ...

Q: Calculus Question

A: Since both the variables are a function of t, we differentiate the expression with  respect to t.

Q: 41

A: f(x) = x - 2sinxHence, f'(x) = 1 -  2 cosx

Q: see attachment

A: Given: -

Q: If the instantaneous rate of change of f(x) at (4, −9) is 8, write the equation of the line tangent ...

A: From the given statement, the rate of change of f(x) at (4, –9) is 8.That is,  f′(x) = 8.

Q: Use implicit differentiation to find y' Then evaluate y' at (3,5) 3x2-y2-2 0 y' = y'l3.5) y'la5)= En...

A: Differentiate with respect to x,

Q: Calculus Question

A: The given function is,

Q: Find an equation of the tangent to the curve at the given point. x 3 , y = t2 3, (3, 4)

A: Given curve is 

Q: The manager of Dixie Furniture Company estimates that the daily output of her factory (in thousands ...

A: a.The given function is

Q: It is determined that the temperature​ (in degrees​ Fahrenheit) on a particular summer day between​ ...

A:

Q: find the differential of each function

A:

Q: 10, 11, and 12 Simplify the expression. 10. tan(sin)

A: Simplify the expression

Q: Find the higher order derivatives for f (x)=x^5, what is f^(6) (x)?

A: According to the given information f(x) = x5 and it is needed to calculate f6(x).Since, if p(x) is a...

Q: Exercise 3: Use the squeeze theorem to prove lim0 sin(x-1) = 0

A: To prove:

Q: A company's profit P (in dollars) from selling x units of product can be modeled by  P (x)=500x-(1/2...

A: To work out the rate of change of the required variable with respect to time, using the given data

Q: A piece of wire 18 m long is cut into two pieces. One piece is bent into a square and the other is b...

A: Let x m make a square.So each side= x/4 mArea of the square = (x/4)^2= x^2/16 m^2

Q: Find the derivative. f(x)x (2x+1)

A:

Q: Exercise 5: Sketch a graph with all of the following properties dom(f) [5,5]; .f is discontinuous at...

A: Refer to the question we need to sketch the graph of such function which has all the provided proper...

Q: If C(x) is the cost of manufacturing an amount x of a given product and $12 is the price per unit am...

A: To find the maximum profit, if C(x) is the cost of manufacturing an amount x of a given product and ...

Q: Clolot301-10m 13(01 rttErE13t)EEATHETK 2. 37 Fnd the tandenttal and norma acceratiaK rE=(2F hon c on...

A:

Q: An underground gasoline storage tank is leaking. The tank currently contains 600 gallons of gasoline...

A: Consider the given informationThe tank currently contains 600 gallons of gasolineGasoline losing 3.5...

Q: Use implicit differentiation to find dy/dx and d2y/dx2 4 sqaureroot y=x-5y

A: Given, function is

Q: see attachment

A: Consider the given function of temperature:

Q: How do I find the velocity? I tried taking the anti deravative of a(t) twice but it didn’t match the...

A: The given acceleration is

Q: show work to prove if the serie is convergent or divergent?   as n=> infinity   an= (ln(3n)) / (3...

A: The given series is,

Q: i need help with part d)

A: As per norm, the first three questions are answered. To study the given model for s(x) and its deriv...

Q: 2 dx 43.

A: Given integral is 

Q: Number 8

A: first find the derivative.

Q: How do you use implicit differentiation to solve:  tanxy=x+y   at point (0,0)

A: The given expression is,

Q: Use implicit differentiation to find y' for the equation below y2 +5y+ 9x 0 Use implicit differentia...

A: Given equation is 

Q: Give the derivative formula for the function g(x) 2.8x12 = (x), 6

A: The given functions are,

Q: Find the derivative 3x (x4+ 1)5 dx d 3x (x4 + 1)5]- dx

A: To find the derivative of [3x·(x4 + 1)5]

Q: Sketch the solid described by the given inequalities: 0<=r<=2, -pi/2<=theta<=pi/2, 0<...

A: First draw the first two inequality 0<= r <=2 and –pi/2<= theta <= pi/2 in the xy-plane....

Q: Calculate the derivative of the function y=(x6+2)x  ​(i) using the fact that bx=exlnb and​ (ii) by u...

A: Given function is ,    

Q: Determine where the graph of the function is concave upward and where it is concave downward. (Enter...

A: Given, function

Q: Differentiate the function. h(x) 13 csch (x3) Give your answer in exact form. 39x2 39х h(x) = 6 х

A:

Q: A forest ranger is in a forest 2 miles from a straight road. A car is located c miles down the road....

A:

Q: х _ у Consider the function f(x, y) = 3 - using each given vector v. Find D.,f(5, 5), where u = v i ...

A: Since we only answer up to 3 sub-parts, we’ll answer the first 3. Please resubmit the question and s...

Q: lim In(10x) x-0t

A: To find the below right-hand limit.

Q: A ladder 10 ft long rests against a vertical wall. If the bottom of the ladder slides away from the ...

A: It is given that,

Q: Edt re =sect tEH), tne Fnd the eh of the cure re)- ti,ee 3 0te 2-1

A: To determined the arc length of the parametrized curve between the given limits

Q: x = t3 − 12t,    y = t2 − 2 find d2y dx2 and for which values of t is the curve concave upwa...

A: We find dx/dt and dy/dt. 

Q: Use polar coordinates to find the limit. [Hint: Let x = r cos(θ) and y = r sin(θ), and note that (x,...

A: Given information:

Q: A publishing company estimates that when a new book by a best-selling author is introduced, its sale...

A: As per norms, the first three questions are answered. The problem concerns applying basic rules of d...

Q: Calculus Question

A: Consider the given value of the question,

Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.