25,270 Answered Questions for the topic calculus

Calculus

06/22/23

Can Rolle's theorem be applied or no?

Determine whether Rolle's theorem can be applied to f on the closed interval [a, b]. (Select all that apply.) f(x) = −x2 + 6x, [0, 6]Yes, Rolle's theorem can be applied.No, because f is not... more
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Calculus

06/22/23

Country Day invested in stocks. Country Day invested in bonds. Country Day invested in CDs.
Country Day's scholarship fund receives a gift of $ 165000. The money is invested in stocks, bonds, and CDs. CDs pay 5 % interest, bonds pay 5.6 % interest, and stocks pay 9 % interest. Country day... more
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Calculus

06/22/23

find dy for the given values of x and delta(x) y=1/x, x = 10 delta(x) -0.003
find dy for the given values of x and delta(x) y=1/x, x = 10 delta(x) -0.003
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Calculus

06/22/23

Number of Newspaper ads to run is? Number of Radio ads to run is? Maximum target group exposure is?
A company has $9,510 available per month for advertising. Newspaper ads cost $100 each and can't run more than 23 times per month. Radio ads cost $520 each and can't run more than 31 times per... more
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Calculus

06/22/23

Number of Newspaper ads to run is? Correct Number of Radio ads to run is? Maximum target group exposure is?
A company has $8,470 available per month for advertising. Newspaper ads cost $240 each and can't run more than 21 times per month. Radio ads cost $560 each and can't run more than 28 times per... more
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Calculus Math

06/22/23

The answer is 3. is it true? Help me check the answer. thank you
Given that σ is the part of the surface z=2-x in the first octant from y=0 to y=1. If 𝜓(x,y,z) =x2yz, F(x,y,z)=yi+zj+xk and n is the unit normal vector to the surface pointing outwards, evaluate... more
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Calculus Math

06/22/23

The answer is -3π4 or 3π4 ? Help me check the answer. thank you
Show that the force field F(x,y,z)=(y2z3cosx-4x3z)i+(2z3ysinx)j+(3y2z2sinx-x4)k is conservative and find its potential function. Hence find the work done by F(x,y,z) in moving an object from... more
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Calculus Math

06/22/23

The answer is 2π-4 is it true? Help me check the answer. thank you
If C is the boundry of the region bounded above by the curves x2+y2-2x=0 and below by y=x, use Green's theorem to evaluate:∮C(xesinx -3y)dx+(5x+ In(y+1))dy
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Calculus

06/22/23

Country Day invested in stocks. Country Day invested in bonds. Country Day invested in CDs.
Country Day's scholarship fund receives a gift of $ 195000. The money is invested in stocks, bonds, and CDs. CDs pay 3.5 % interest, bonds pay 3.1 % interest, and stocks pay 8.3 % interest. Country... more
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Calculus

06/22/23

AP Calculus BC question
find the limit using lim x->0 sinx/x = 1 lim x->0 (sin3xcot5x)/xcot4x
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Calculus

06/22/23

Estimation Instantaneous rate of change
Estimate the instantaneous rate of change of the function f(x) = xlnx at x = 18 and x = 19.f'(18) ≈f'(19)
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Calculus

06/22/23

Calculus Diagonalization
Given that the matrix A has eigenvalues v1=−8 with corresponding eigenvector v1 = [1][2]and v2 with corresponding eigenvector v2 = [2][3] find A
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Calculus

06/22/23

Calculus Diagonalization
M = [11 2] Find formulas for the entries of Mn, where n is a positive integer. [-4 5]
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Calculus

06/22/23

Calculus Diagonalization
Give an example of a 2×2 matrix with no real eigenvalues.
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Calculus

06/22/23

Calculus Diagonalization
Suppose a 3×3 real matrix A has only two (real) distinct eigenvalues. Suppose that tr(A)= −4 and det(A)= −32. Find the eigenvalues of A with their algebraic multiplicities.
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Calculus

06/22/23

Calculus Diagonalization
A = [-7 -0.25] Find an invertible matrix X and a diagonal matrix D such that X-1AX=D [48 1]
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Calculus

06/22/23

Calculus Diagonalization
A = [-47, -21] Find S,D and S-1 such that A = SDS-1 [98, 44]
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06/21/23

Find the sum of the following convergent series: a)∑_(n=1)^∞ n/(n+1)! b) (∑_(n=1)^∞ 2/5^n)-(∑_(n=1)^∞ 3^n/5^n)
Can you help me with this problem step by step. Usually I dont have problems with these but now I don't understand nothing
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06/21/23

"Study the convergence of the series whose first terms are as follows: 1/2 + 7/9 + 13/28 + 19/65 + 25/126 + ...
Can you help me find the answer of this problem step by step so I can understand? Thank you!
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06/21/23

Here are the first five terms of a sequence: 3/5, 3/4, 12/11, 12/7, 48/17, ... a) Find the general term. b) Determine if this sequence converges or diverges. If it converge, state the number

can u help me with these questions by showing me the answer setp by step. I dont really understand.
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06/21/23

Expand the function f(x) = 1/x + 3 into a Taylor series around a = -2 and determine the interval of convergence."
Hi, I dont really understand this questioon can you give me the answer step by step so I can understand how to solve this problem
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Calculus

06/21/23

Calculus of a function and its inverse
Suppose f(x) is an invertible, differentiable function and f(3) = -3, f(-3) = 1, f '(3) = 4, and f '(1) = 5. Find (f-1 ) ' (-3), that is, find the value of the derivative of f -1 (x) at x = -3.
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06/21/23

Precalculus Question: Are my answers for the following problems correct?
Question 1: You want to hang a 600 pound statue from your ceiling for a party. It will be hung by two cables each making a 60 degree angle with the ceiling. How much tension will be in each of the... more
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Calculus

06/20/23

Squeeze theorem problem
Use the Squeeze theorem to prove lim(x→∞) 1/x+e-x = 0For x ≥ 0, since 0 < e-x ≤ 1, we have_____ < x + e-x < _____Therefore, _______ < 1/x+e-x < _______please fill in the blanks and... more
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Calculus Math

06/20/23

Calc 3 question
Find Z_t and Z_p for Z = 4ysin(2x), x = 3u - P, y = (P^3)(u), u = t^2 + 1.
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