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By justifying your answer determine whether the function T is a linear transformation.
T:P3→ P4defined as T(a+bx+cx2+dx3)=b−ax+adx4
T:P3→ M2,2 defined as
T(a+bx+cx2+dx3)= [−d,c,√3a,a+b] its a matrix
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In each case, compute the derivative dy dx . Do not simplify your answer.
a) y= 4x^3e^5x
b) y=ln {(x^3 + 3x)(2x^4 -1)} using product rule
c) f (x) = x^4 ln 3x - 2/ e^2x
d) y= ln(2x^3)/ (4x^2-1)
Please show all work and label answers according to question number / letter
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What is the radius of convergence for (( 2x-3)^n) / (n+4)^2 * 5^n+1
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part A)The antiderivative of an acceleration function is a position function.
A)True
B)False
Part B)A right Riemann sum always gives an underestimate.
A) True
B) False
Part C)Integration by substitution is the process that reverses the chain rule.
A) True
B) False
Part D) The derivative of an indefinite integral returns the original function.
A) True
B) False
Part E) The antiderivative of a constant is linear.
A) True
B) False
Part F) Suppose you want to estimate the area under a function f ( x ) from x = 2 to x = 6 using a Riemann sum and n = 2 rectangles. What is Δ x ?
A) 2
B) 1
C) 4
D) 3
Part G) To compute
∫ ( 2 x + 5 ) e x 2 + 5 x d x
what substitution would you need to make?
A) u=2x+5
B) u=x2+5x
C) u=x
D) None of these answers are correct.
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Find the point on the curve y=4x+4 closest to the point (0,8)
(x,y)=
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(18) The region is bounded by y = 2 − x 2 and y = x.
(a) Sketch the region.
(b) Find the area of the region.
(c) Use the method of cylindrical shells to set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region about the line x = −3.
(d) Use the disk or washer method to set up, but do not evaluate, an integral for the volume of the solid obtained by rotating the region about the line y = 3.
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The owner of a luxury motor yacht that sails among the 4000 Greek islands charges $688/person/day if exactly 20 people sign up for the cruise. However, if more than 20 people sign up (up to the maximum capacity of 90) for the cruise, then every fare is reduced by $8 for each additional passenger.
a. Assuming at least 20 people sign up for the cruise, determine
how many passengers will result in the maximum revenue for the
owner of the yacht.
b. What is the maximum revenue?
c. What would be the fare per passenger in this case? (Round your
answer to the nearest dollar.)
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6.3 3a. Find an approximation of the area of the region R under the graph of the function f on the interval [−1, 2]. Use n = 6 subintervals. Choose the representative points to be the left endpoints of the subintervals. f(x) = 6 − x2
_________square units
b. Find an approximation of the area of the region R under the graph of the function f on the interval [1, 3]. Use n = 4 subintervals. Choose the representative points to be the right endpoints of the subintervals. f(x) = 6/x
_________ square units
c. Find an approximation of the area of the region R under the graph of the function f on the interval [0, 3]. Use n = 5 subintervals. Choose the representative points to be the midpoints of the subintervals. (Round your answer to one decimal place.) f(x) = 3ex
___________square units
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The joint density function for random variables X, Y, and Z is
f(x, y, z)= Cxyz if 0 ≤ x ≤ 1, 0 ≤ y ≤ 2, 0 ≤ z ≤ 2, and f(x, y, z) = 0 otherwise.
(a) Find the value of the constant C.
(b) Find P(X ≤ 1, Y ≤ 1, Z ≤ 1).
(c) Find P(X + Y + Z ≤ 1).
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What is the meaning of Δy/Δx? What is its geometric interpretation? What is the meaning of dy/dx? What is its geometric interpretation?
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Compute the derivative of the given vector field F. Evaluate the line integral of
F(x,y,z) = (y+z+yz , x+z+xz , x+y+xy )
over the path C consisting of line segments joining (1,1,1) to (1,1,2), (1, 1, 2) to (1, 3, 2), and (1, 3, 2) to (4, 3, 2) in 3 different ways, along the given path, along the line from (1,1,1) to (4,3,2), and finally by finding an anti-derivative, f, for F.
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| Find the flux of the vector field F = x i + e2x j + z k through the surface S given by that portion of the plane 2x + y + 8z = 7 in the first octant, oriented upward. |
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Calculate the all of the second order derivatives of f(x,y)=x^4 y- 〖3x〗^4 y^3+5y-10
Let be f(x,y,x)=2x^5 yz^3-3x^(-4) y^3 calculate the f_xyz=?
If f(x,y,z)〖=5e〗^(-xyz^6 ) +lnx calculate the f_yxz=?
Let f(x,y)=cos(x^3 y) ise df/dx=? df/dy=?
z=2x+y , x=sin(3t ) and y=cos(3t) using the chain rule calculate the dz/dt where t=π/2.
Find the critical points of the f(x,y)=〖6x〗^2+12y^2+12x-24y and provide the information about the critical points obtained (if it is max, min or saddle point).
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