A cylindrical tank with radius 6 m is being filled with water at a rate of 2 m3/min. How fast is the height of the water increasing? Step 1 If h is the water's height, the volume of the water is V = tr2h. We must find dV/dt. Differentiating both sides of the equation gives the following. dh dV = tr2 dt dh dt dt Step 2 Substituting for r, this becomes dV 367 dt dh dt 367 Step 3 dV dh we can conclude that the height of the water is increasing at the following rate. dt Substituting for and isolating dt 1 dh m/min. dt 12n

Q: Let (M; d) be a metric space. Show that the set {B(x; 1=n); x ∈ M; n ∈ N*} is a Basis for the metric...

A: Given :  (M; d) be a metric space. To Show :  the set {B(x; 1=n); x ∈ M; n ∈ N*} is a Basis for the ...

Q: Express w as a linear combination of u and v: ? = (4,1), ? = (−2, −1), ? = (2, −2)

A: Let w = (4,1) u = (-2,-1) v=(2,-2) we can write this as: u-21 + v2-2 = 41   -2u + 2v = 4 u - 2v = 1 ...

Q: The great Swiss mathematician Leonhard Euler sometimes reached incorrect conclusions in his pioneeri...

A:

Q: Use the shell method to set up and evaluate the integral that gives the volume of the solid generate...

A:

Q: Use the ratio test to find the radius of convergence of the power series. 00 4x" Σ n=0 3" (n+ 1)

A:

Q: Given the graph of f(x) below, determine which statements are true and which are false. a. lim f(...

A: From the given graph we need to find the limit.

Q: For the linear function y = f(x) = 3x + 10: df at I dr a. Find -7. f'(-7) = b. Find a formula for I ...

A: For (a), dfdx=f'(x)=-3x+10' =-3 So, f'(-7)=-3. For (b), We need to find a formula for x = f-1(y). y=...

Q: L = of €2.10 %3D 6

A: 1/6 of € 2.10 is

Q: Find the maximum rate of change of f(x, y) = In(x² + y?) at the point (-4, -3) and the direction in ...

A:

Q: Evaluate the limit lim CSC X

A:

Q: . Given the graph of g(x) = {√−x−2+1, x<-2   x2+2x+5,  x≥-2 below, evaluate its limit as x approache...

A: Given that: 5. g(x)=-x-2+1, x&lt;-2x2+2x+5,     x≥-26. g(x)=Graph is given.7. g(x)=-1x2

Q: Extension Question 1: If the inside of the composition of the logarithm is quadratic, what portion o...

A:

Q: Find the slope of the tangent to the curve, y = 2x – x² +x° at (0,2).

A: Given curve is  y=2x-x2+x3.  We have to find slope of the tangent to the curve , at (0,2 ). To find ...

Q: (-5sin t) dt

A:

Q: Determine the general solution for each given higher-order differential equation or particular solut...

A: Here we have to find out the solution of the given differential equation

Q: 2000 A television camera at ground levell is 2000 feet away from the launching pad of a space rocket...

A:

Q: Given the function: f(x,y, z) = x°y2² + æy° +y°z Find а. fazy: (x, y, z) b. fazyz(1, –1, 1) -

A: Given the function :  f(x,y,z) = x3y5z7 + xy2 + y3z

Q: 3. Suppose a feather is dropped from a height of 40 m above the surface of the moon, its height s (i...

A:

Q: 1. Let y be the part of the curve y =r² running from (-1,1) to (2,4). Calculate ry dr + (x+ y) dy.

A:

Q: Test the series for convergence or divergence. 3"n! 13 · 18 · 23 ... (5n + 8) n=1 Use the Select v a...

A:

Q: Sketch the graph and find the area bounded by the curves for y = 2x² and y = x² + 4

A: Given query is to find the area bounded by the curves.

Q: an+1 Assume that an converges to p = 1. What can you say about the convergence of the given series? ...

A:

Q: Write the first five terms of the sequence: {Vn² +n – n}, n=1 Determine whether the sequence converg...

A: given sequence n2+n-n1∞  

Q: Solve 3y fip %3D dr 2x

A:

Q: Find the linear approximation L(x) of the function f(x) = /1 - x at a = 0. L(x) = Use L(x) to approx...

A:

Q: 1. Find the length of the curve r(t) = (sin 2t, cos 2t) from t 0 to t = 2n. %3D 2. Find the length o...

A: As we know that, The expression for the length of vector-valued curve is: L=∫abx't2+y't2dt   1). Giv...

Q: use implicit to tind the eguation of the tangent line tothe Ealloming differentiation Curve at' the ...

A: Topic = Derivative

Q: 2. Use central difference approximations to estimate the first and second derivatives of y = e* at x...

A:

Q: A pole stands 75 feet tall. An angle is formed when wires of various lengths of aF feet are attached...

A: Given that length of a pole is 75 ft.  find the rate of change of the angle dθdx  at x=199ft

Q: d²f , df_ (a) +5- - + 6f =0, f(0)=1, f(0) =- 4 dt? dt

A:

Q: The graph of f(x) is given by 3 Determine the following limits. Write your 2 answer in the form lim ...

A:

Q: The e half- lite of a ra to actine material 1S lle years. Sunppose we have a 10amg sa, How much of t...

A: Given:   T = 110     N0 = 100     t = 30

Q: 9. | cos (2r) dt

A:

Q: Determine whether the improper integral converges and, if so, evaluate it. (Use symbolic notation an...

A: Let's find. 

Q: (a) Find the series' radius and interval of convergence. Find the values of x for which the series c...

A:

Q: Find the absolute maximum and the absolute minimum of f(x,y)= 3xy-3x-6y+1 on the closed triangular r...

A: Given:- The function is, f(x,y)=3xy-3x-6y+1on the closed triangular region whose vertices are (0,0),...

Q: Write the equation of a sine function that has the given characteristics. The graph of y = x, shifte...

A: Given a function f(x),a new function g(x)=f(x)+k,where k is a constant, is a vertical shift of the f...

Q: Find the abs extrema as well as all values of x where they occur for the domain.   f(x)= x/12 + 1/...

A:

Q: Let y be the part of the curve y = x² running from (-1,1) to (2,4). Calculate xy dx + (x + y) dy.

A: (1)

Q: Solve eX =9 for x. ... The solution is x (Type an integer or decimal rounded to four decimal places ...

A: Consider  ex=9

Q: Show that V is not a subspace of R°: V is the set of all (x, y, z) such that x + y +z = 3

A:

Q: integral f theta^2  cos 3(theta)   d theta

A:

Q: Find the missing values assuming continuously compounded interest. (Round your answers to two decima...

A:

Q: Find y'' by implicit differentiation 4x3+3y3=6

A:

Q: a) Evaluate in terms of Gamma function ∫e^(−y^2) y^13 dy   limit 0 to ∞ b) Find ∫f(x) dx limit: 1 t...

A:

Q: 4. y=ysin 2xcos 5x + 3

A: Find your answer below 

Q: h3-4h 3. lim h-2 h3-2h2

A:

Q: Use the Ratio Test to determine if the following series converges absolutely or diverges. E (- 1)nn ...

A:

Q: Answer the following True or False: If g(x) is the inverse of a differentiable function f(x) with de...

A: Find your answer below 

Q: Test the series for convergence or divergence. 3.7.11 (4n – 1) · (5n – 1) * 4. 9. 14... n=1 Part 1: ...

A: