08/15/24

suppose set a contains 55 elements and set b contains 54 elements. if set a and b have 16 elements in common, what is the total number of elements in either set a or set b

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06/16/24

Calculus help question
Find an antiderivative F(x) with F′(x)=f(x)=5+28x3+21x6 and F(1)=0. Remember to include a "+ C" if appropriate.
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08/02/23

Use the definition of derivative to find F ' (x) given that

Use the definition of derivative to find F ' (x) given that F(x)=2x2-5x+3 (do NOT use the short cut method). Use the result to find the slope of the tangent line at the point (-1, 10).
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08/02/23

Find F ' (x) given that
F(x)= (2x3+3x2-5)(5x2-2x+1)
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06/28/23

Find the volume of the solid obtained by rotating the region bounded by the curve y = sin ( 6 x 2 ) and the x -axis, 0 ≤ x ≤ √ π 6 , about the y -axis.
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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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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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06/20/23

The answer is 9π. is it true? help me check the answer. thank you
If F (x,y,z)=tan z i +(x+z)j+xsiny k and σ is the portion of the cylinder z=9-x2-y2 above the xy-plane oriented so that the unit normal vector n points to the outside of the cylinder, use Stoke's... more
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03/05/23

Real Analysis: Completeness Axiom
Suppose that k > 0 and S is a subset of R is a bounded set. For any set S, we define k * S = {k * x: x is an element of S}. Show that sup (k * S) = k * sup (S). a) Show that sup (k * S) <= k... more
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02/27/23

Show that det(A) ≤ a_{11}a_{22}· · ·a_{nn}, where A is positive semidefinite and a_{11}, a_{22}, · · ·, a_{nn} are the diagonal entries.
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02/27/23

Show that if AB is invertible, so is A. Hint: there is a matrix W such that ABW = I.
Show that if AB is invertible, so is A. Hint: there is a matrix W such that ABW = I.
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02/22/23

Show that if the columns of B are linearly dependent, then so are the columns of AB.
Show that if the columns of B are linearly dependent, then so are the columns of AB.
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02/21/23

How do you prove this by induction?
Prove Bernoulli’s inequality by induction: For an arbitrary x ∈ R, such that x ≥ 1, prove by induction on n that (1 +x)n ≥ 1+nx for any positive integer n.
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02/16/23

Prove by induction that every integer n, n >=0, can be represented by 5a + 7b for a,b in Z
I'm having trouble approaching this by induction.I prove the base case in that if n = 0, 5a + 7b = 5(0) + 7(0) = 0I assume that 5a + 7b = n is true, then I try to show that it holds true for n+1.... more
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02/07/23

Intergrals calculus

∫ from 1 to √3 6 / ((tan−1(𝑥))(1+𝑥^2) )𝑑𝑥
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01/22/23

Continuous Functions
Let f(x) = {7x-5 if x < -4 {-8x+b if x ≥ -4If f(x) is a continuous function everywhere, then we must have...b =
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01/18/23

Find the inverse Laplace Transform for F(s)=1/ s(s^2+6s+5)
Please help me sir/madam, question : Find the inverse Laplace Transform for F(s)=1/ s(s^2+6s+5)thank you.
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12/27/22

Orthogonality question from Linear Algebra
a) Let u1,u2,u3 are vectors in RN. Suppose that vectors u1, u2 are orthogonal and the norm of u2 is 4 and uT2.u3 = 7. Find the value of the real number 'a' in u1= u2 + au3.b) Let S =... more
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11/22/22

MacLaurin Series From Binomial Series Formula
Use the following binomial series formula: (1+x)^m = 1 + mx + [m(m−1)x^2]/2! + ⋅⋅⋅ + [m(m−1)⋯(m−k+1)x^k]/k! + ⋅⋅⋅to obtain the MacLaurin series for1/[(1+x)^9] = ∑k=0 to ∞ _______
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10/21/22

using implicit differentiation, find y' for sin(x) + sin(x)sin(y) = cos(xy)
I tried it multiple times but couldn't get the right answer, so could someone show me the specific steps for this question?Thanks!
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10/19/22

Find the integral of 7 csc^3(x)/ (tanx) dx
Find the integral of 7 csc3(x) / tan(x) dx
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07/29/22

Let 𝑎, 𝑏 ∈ ℤ and 𝑚 ∈ ℕ. Prove that if 𝑎 ≡ 𝑏(mod 𝑚), then 𝑎 3 ≡ 𝑏 3(mod 𝑚).
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07/15/22

Find how many meters traveled during first t seconds

A particle that moves along a straight line has velocityv(t)=t^(2)e^(−4t)meters per second after t seconds. How many meters will it travel during the first t seconds (from time=0 to time=t)?
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07/11/22

1. Use the shell method to find the volume of the solid generated by revolving the region bounded by the given curves and lines about the y-axis.
y = 2x3, y = 2x, for x ≥ 0A) 4/15 πB) 2/15 πC) 8/15 πD) 4/5 π
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07/04/22

Critical numbers

Consider the function: √t^2-4 this whole thing is under the square root.How would I go about figuring out where the function is increasing or decreasing. I've already got the derivative and set it... more
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