An metal cube with each edge of length s millimeters is expanding uniformly as a consequence of being heated. (a) Find the average rate of change of the volume of the cube with respect to an edge as s increases from 5.0 to 5.1 mm. Do not round your answer. average rate: 76.51 mm³/mm (b) Find the instantaneous rate of change of the volume of the cube with respect to an edge at the instant when s= 5 mm. Do not round your answer.

Q: Find the absolute maximum and minimum of f(x,y)=4x+3y within the domain x^2+y^2≤16 Please show your…

A: Concept: Absolute maxima of a function refers to its highest point within its whole domain, whereas…

Q: Find the absolute maxinum and minimum values of the function over the indicated interval, and…

A: Here, the given function is: f(x)=8x+3 which is a linear function. So, it has no critical point.…

Q: 3. Classify the graph of the equation as a circle, parabola, an ellipse, or a hyperbola. (a) 16x² -…

A:

Q: Find the critical point of the function. Then use the second derivative test to classify the nature…

A:

Q: Evaluate the definite integral. [²³ sin5(x) dx Step 1 6.² sin5(x) dx, first rewrite the integral. To…

A:

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim (ti+ sin(t)j + cos(t)k)…

A: The objective of the question is determine the limit.

Q: The graph of f is shown. Apply Rolle's Theorem and find all values of c such that f '(c) = 0 at some…

A: The graph of f is shown. To apply Rolle's Theorem and to find all values of c such that f'c=0 at…

Q: A store is deciding what types of fruit to stock nearest to the registers. They can either stock…

A: Let's find maximum potential revenue fruit.

Q: 10 15 20 25 30 monthly salary S( t) in dollars for a dock worker shown above has the following cubic…

A: Please refer to the image below

Q: A car rental agency rents 480 cars per day at a rate of $20 per day. For each $1 increase in rate,…

A: Solution: Car rented =480 -10x rate =20+x

Q: the open interval on which the function is increasing or decreasing. (Enter your answers using…

A: Topic:- function and application of derivatives

Q: 8. Show the following limit does not exist: ay +1 lim (au)-(1,-1) 22²-2²

A:

Q: A large tank is filled to capacity with 700 gallons of pure water. Brine containing 3 pounds of salt…

A:

Q: Find the inverse Laplace transform of the given function. F(s) = 5e-2s s² - 25 Use uc (t) to denote…

A:

Q: Task 1: Consider vectors x1and x2. For this task. you can only adjust the weights c1and c2by moving…

A: (a) x1→=-11  , x2→=21⇒c1x1→+c2x2→=00

Q: Use Definition 7.1.1, DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t≥ 0. Then…

A: Given figure:-

Q: Let a and b denote two sides of a triangle and let 8 denote the included angle. Suppose that a, b,…

A:

Q: f(x) is continuous on (-∞,∞). Use the given information to sketch the graph of f. f'(0) = 0, f'(-11)…

A:

Q: Question 19 Let F(x) -1. √1+t¹ dt for x in (-∞0, ∞o). Find F'(- 5 sin z O F'(x) = -√1 + cos²x O…

A:

Q: Describe the graph of the equation: r = 6ti − 9j + (1 + 8t)k. [Choose the correct answer.] O The…

A:

Q: Answer true or false. If f is not piecewise continuous on  [0, ∞>),  then  ℒ{f(t)}  will not exist.

A: Given problem:- If f is not piecewise continuous on [0, ∞),then ℒ{f(t)} will not exist.  True…

Q: Find the second-order partial derivatives of the function. Show that the mixed partial derivatives f…

A:

Q: object from v? If yes, explain how would you recover s. If not, what other information are we…

A:

Q: 3 (1 + 2x - 4x³) dx

A: The given integral is ∫131+2x-4x3dx

Q: = 4 sec 0. Find the Cartesian equation for the polar curve r =

A:

Q: Find dy/dx without changing the form of the given function and answer must be in the simplest form:…

A:

Q: Use the definition of the Laplace transform to find L{f(t)}. (Enter your answer in terms of s.)…

A: laplace transform

Q: Use the graph of f in the figure to the right to complete parts (A) through (M) (assume that f''(0)…

A: Given: f''(0)<0,f''(b)>0 and f''(g)>0 From graph: f'(a)<0,f'(b)=0, f'(0)=0, f'(g)=0 and…

Q: product

A: Please refer to the image below

Q: ² x (√x + √x) dx

A: We know that integration power rule is  Integration of xn is xn+1/n+1 + C. Here C is integration

Q: A particle moves along a line with a velocity v(t) = -t² + 3t - 7, measured in meters per second.…

A:

Q: Problem 4.14 Find f if 3 f"(x) = 20x³ - 12x² + 6x

A: NOTE: Refresh your page if you can't see any equations. . take integration on both sides

Q: f(x) is continuous on (-∞,∞o). Use the given information to sketch the graph of f. f'(x) +++ 0…

A:

Q: Problem 2 √√x-3 x-9 For the function above, please find the following: a) The domain of the function…

A: NOTE: Refresh your page if you can't see any equations. . as we know, the denominator cannot be…

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

A:

Q: Find a differential equation whose general solution is y = C₁e6t + c₂e-4t y" - 2 y' - 24 = 0 X

A: The solution of the DE is: y=c1e6t+c2e-4t where the solutions to the auxiliary equation are 6 &…

Q: Consider the following. x = sin(10), y = cos(0). (a) Eliminate the parameter to find a Cartesian…

A: Given problem:- x=sin(θ/2) , y=cos(θ/2) , -π≤θ≤ π  Eliminate parameter and find Cartesian equation…

Q: Find the specified nth term in the expansion of the binomial. (x + 2z)?, n = 6

A:

Q: 1) Evaluate the following expressions. 1) sin-1 COS 17 9

A:

Q: Use the equation to find the initial population. Step 1 To find the initial population, substitute t…

A: NOTE: Refresh your page if you can't see any equations. . the given logistic function is

Q: Gravel is being dumped from a conveyor belt at a rate of 40 cubic feet per minute. It forms a pile…

A:

Q: Solve the equation on the interval 0≤0<2t cos 05 (20-7)=1 What are the solutions in the interval 0…

A:

Q: Find the principal unit normal vector to the curve at the specified value of the parameter. 6 r(t) =…

A:

Q: S 2 x ²4x³-5 X e cote 4x³-5 dx

A: The objective of the question is evaluate the indefinite integral.

Q: The position vector r describes the path of an object moving in space. Find the velocity v(t), speed…

A: Given data÷   rt=&lt;etcost,etsint,et&gt; Useful formulas÷   Velocityvt is given by÷ vt=r't Speed is…

Q: Find curl(2z + 3x j + 6y k). curl(2z i+ 3xj+ 6y k) = (i )i + (i )j + ( i )k

A:

Q: lim, 0 6 tan² (5x) 15x²

A:

Q: A spherical snowball is melting in such a way that its radius is decreasing at a rate of 0.1 cm/min.…

A:

Q: The temperature of a cup of coffee varies according to Newton's Law of Cooling: T-K(T-A), where T is…

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

Q: Question 8 Find f'(a) for f(a) O f'(x) O f'(x) O f'(x) = O f'(x) O f'(x) cos - 1 cos? an cos - cos 2…

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