(8) Use the three properties of continuity to show that the function below is continuous at t = 3 g(t) = t² + 1 t+2

Q: A particle starts at the origin, moves along the x-axis to (2, 0), then along the quarter-circle x²…

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

Q: The graph of f' is given below. 2 -2 2 Then f has a local maximum at x = 1. O True False + . f'(x) 6…

A: Graph of f'(x) We have to find at x=1 f has local maxima  or not

Q: H/F.. F. dr, where C is given by the vector function r(t) Evaluate the line integral F(x, y, z) = (x…

A: line integral

Q: The function f(t) = 1100t-100t² represents the rate of flow of money in dollars per year. Assume a…

A: ft=1100t-100t2 Assume a 10-year period at 5% compounded continuously. t=10r=5%=0.05

Q: Graph function y= 2x and y= log2^x on a single set of axes.

A:

Q: If 0 = 1TT 4

A:

Q: Learning Target IA2: I can compute the volume of a solid of revolution using the method of…

A:

Q: xsinx-x² lim x-0+ (ex-x-1)² A) 0 =? B) 2 1|2 D) 2/3

A:

Q: Find the mass and center of mass of the triangular lamina with vertices (0, 0), (0, 3), and (3, 3)…

A:

Q: North Mountain is a neighborhood in Phoenix, Arizona. The square footage and selling prices of 16…

A: The square footage and selling price of 16 randomly selected homes for sale in North Mountain are…

Q: A collector of antique motorcycles is planning to enclose an exhibit in the shape shown below. The…

A: The sides with length x will use a material that costs $5 per foot while the sides with length y…

Q: I. Find the inverse of f(x). Determine the domain and range of f(x) and f '(x). 1. f(x) 2. f(x) = 6x…

A:

Q: Subject: calculus a plane landed in arizona at 4:30pm it left w ashing ton at 12pm how long…

A: Given A plane left washington at 12 pm this plane landed in Arizona at 4:30pm

Q: ii) the evaluation of ffdzdxdy is 2.

A: Given triple integral ∫-11∫y21∫0x2dzdxdy

Q: The number of milligrams D (h) of a certain drug that is in a patient's bloodstream h hours after…

A:

Q: Find the average value fave of the function f on the given interval. f(x)=√x, [0, 25]

A: Given,

Q: Q9 Determine which function has an absolute maximum. (a) f(x) = x³ + 2x - 1 (c) f(x) = x² - 2x + 7…

A:

Q: Use cylindrical coordinates. Evaluate JJJ. √x² + y2 dv, where E is the region that lies inside the…

A: Triple integral having √(x2+y2) dv  Region x2+y2=9 and plane z=3 and z=4

Q: Find the solution of the following initial value problem. 1 1 3 v'(x) = 8x - 8x ; v(8)=52, x>0 The…

A:

Q: -20 20 |ច -20- 20

A:

Q: Given that A (1, 1) is a critical point of the function f(x, y)=2x² - 4xy + y +2.Then: a. A is a…

A:

Q: Name Period 4. Find all angles, 0 ≤0 < 360°, that satisfy the equation below, to the nearest soth of…

A: Here given that :- Sin(θ) = √(3) /4. We find all angles , 0&lt;=θ&lt;360°

Q: Find the sum of the convergent series by using a well-known function. (Round your answer to four…

A: Here given that a conversant series and we find the sum of this series by using a well-known…

Q: Rate oil is pumped out (millions of barrels/month) -Select- Select- 40 35 30 Use the graph of r(t)…

A: Since you have posted a question with multiple sub parts, we will provide the solution only to the…

Q: We know that a= 23 sin' (ax) cos(ax) dx = sin³ (ax) b Find b + C

A:

Q: (b) L-¹268 32-68+12.

A: Given that :      L-1[(s-3)/(s2-6s+12)]       We find laplace inverse transform.

Q: der (volume V = r²h) has a constant volume of 100 cubic feet. If its height is second while the…

A: Topic:- application of the derivative  as we know that volume of the cylinder is  volume V = π r2h…

Q: ction represented by the power series. En ².s B ²-8 +8

A:

Q: An equation of the tangent plane to the surface 2z-x²-0 at the point P,(2, 0, 2) is given by: a.…

A: 2z-x2=0 at the point P0(2,0,2)

Q: Let f(x, y, z)=2e' cos(xz). Then the derivative off in the direction of 7-j-k at the point A(0,0,0)…

A:

Q: Find the tangent plane to the equation z = 5y cos(6x4y) at the point (4,6,30) Z=

A: To find the tangent plane to the equation z=5y cos6x-4y  at the point 4, 6, 30.

Q: Identify and sketch the surface (S) of equation z=: 16 your work). (Show all the details of

A: The given equation z=x216+y24. We have to sketch the graph of the surface.

Q: Evaluate the following definite integral. Express your answer in terms of logarithms. €² dx 2 1…

A:

Q: lim (1 t→∞ 12 2 t2

A: Consider

Q: A rectangular flower garden with an area of 70 m² is surrounded by a grass border 1 m wide on two…

A: Let length of flower graden=x mLet width of flower garden=h m

Q: Find the mass and center of mass of the solid E with the given density p. E is the cube 0 ≤ x ≤ a, 0…

A:

Q: Consider the following double integral: 12 1 = [[y²e dy dx 0 2x 1) Sketch the region of integration…

A:

Q: Suppose F(x, y) = (2x – 4y)i + 3xj and C is the counter-clockwise oriented sector of a circle…

A: Given function (2x - 4y)i  + 3xj

Q: 31. The region in the first octant bounded by the coordinate planes, the plane x + y = 4, and the…

A: We have given  Plane x + y = 4  and  Cylinder y2 + 4z2 = 16 we have to find volume using triple…

Q: When recording live performances, sound engineers often use a microphone with a cardioid pickup…

A: Equation of cardioid r=8+8sinθ

Q: = 4+ J₁ Find F'(x). 2t² + 1 t² + 3 dt.

A:

Q: Problem #1 A family of curves is given by x² - y² = k²_for k = {-00,00} Find the equation of the…

A:

Q: Let R be the region enclosed by the curves y = x² - 2x and y=x+4. (Note: one of th curves is…

A: To solve the following

Q: 7. Express the Cartesian coordinates in polar coordinates in two different ways. (2,0) b. (-1, √3)…

A: Express the cartesian coordinates in polar coordinates in two different ways a) (2, 0)  b)…

Q: (a) In Section 2.8 we defined an antiderivative of f to be function F such that F' = f. Try to guess…

A:

Q: Find the gradient vector field of f. f(x, y) = tan(2x - 3y) Vf(x, y) =

A:

Q: ■ If y = Σº。 (k + 1) x²+³ then y² = 0 k=0 k=0

A: The function is given by y = ∑k=0∞k+1xk+3 To determine: The first derivative of the function.

Q: Find the limit 11x³y lim along two different paths. No decimal entries allowed. (z,y) → (0,0) 3x6 +…

A: The given limit limx, y→0, 011x3y3x6+y2. We have to find this limit.

Q: Step 4 To find Step 5 To find dy dx -, we divide dy dt dx dt dy dx d²y dx2' = = dy dt d dt dx -10t +…

A: Write the dydx from step 4

Q: 6. Use a Riemann sum to approximate the area under X the curve y = √√x + 2 for 2 ≤ x ≤ 14 by…

A: