Find the 3rd and 6th approximations of the sum in part a.
Please help. I cannot figure this out.
Open Question: How to use Riemann sums for this expression?
Let f(x)= 2 + x^3 , 1 less then or equal to x less than or equal to 4. Use the idea of Riemann sums to find an expression for the area under the graph of f as a limit. You do not need to evaluate the limit.
Open Question: Let F(x) = ʃ t-3 / t^2+7 dt (from 0 to x) for -oo <x<oo?
I assume you mean F(x) = ? (t-3) / (t^2+7) dt (t = 0 to x) ---> don't forget parentheses
F'(x) = (x-3) / (x^2+7)
F''(x) = (1*(x^2+7) - (x-3)(2x)) / (x^2+7)^2
F''(x) = (-x^2+6x+7) / (x^2+7)^2
F''(x) = -(x+1)(x-7) / (x^2+7)^2
a)
F has minimum value where F'(x) = 0 and F''(x) > 0
F'(x) = 0
(x-3) / (x^2+7) = 0
x = 3
F''(3) = -(3+1)(3-7) / (3^2+7)^2 = 16/16^2 = 1/16 > 0
Minimum value at x = 3
b)
F is increasing when F'(x) > 0
(x-3) / (x^2+7) > 0
x - 3 > 0 . . . . . . since (x^2+7) > 0 for all x
x > 3
F is decreasing when F'(x) < 0
x < 3
Increasing on interval (3, 8)
Decreasing on interval (-8, 3)
c)
F is concave up when F''(x) > 0
-(x+1)(x-7) / (x^2+7)^2 > 0
-(x+1)(x-7) > 0 . . . . . . since (x^2+7) > 0 for all x
-1 < x < 7
F is concave down when F''(x) < 0
x < -1 or x > 7
Concave up on interval (-1, 7)
Concave down on intervals (-8, -1) U (7, 8)
Open Question: Integral Problem! 10 Points Go!?
I've got: Integral from pi/4 to Infinity of (4+cos (4x))/(x^3)dx
This is an example of Convergence, but I don't know how to solve it. Any help, even some kind of basic outline is appreciated. Better yet, if you can lead me through all the steps, that would help out a lot. Thanks SO much!
Open Question: MATHS QUESTION PLEASEEEE HELPPP ME!! IM BEGGING!!?
It is noticed that the height of a cone is twice its radius and that the cones volume is exactly 1000cm63. Calculate the dimensions of the cone correct to one decimal place.
please explain your answer thankyou
Open Question: Newton's Second and Third Law Derivations?
Start with Newton's laws F = ma and F_12 = F_21
Show that if two bodies exert a force on each other, ?p_1 = -?p_2
Show that if two bodies exert a force on each other, ?p_1 = -?p_2
How do I do this?
Also, I think I need to somehow derive the following equation from those:
?P = (m_A * v_fA + m_B * v_fB) - (m_A * v_iA + m_B * v_iB)
Where:
m_A = mass of cart A
m_B = mass of cart B
v_fA = final velocity of cart A
v_fB = final velocity of cart B
v_iA = initial velocity of cart A
v_iB = initial velocity of cart B
Context: This is for a physics lab report due today. In the lab we took two carts (A and B) and pushed them into each other and gathered the initial and final velocities of both carts. We are trying to determine whether or not momentum is conserved.
Any help you could provide will be greatly appreciated. Also if you have any tips for writing this lab report, please include those. Thank you so much!
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