Saturday
April 19, 2014

Homework Help: Math: Calculus

Recent Homework Questions About Calculus

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Calculus
sure you do. It's just a geometric series a = 1/e^2 r = 1/e^2 S = a/1-r = (1/e^2)/(1 - 1/e^2) = 1/(e^2-1)
Thursday, April 3, 2014 at 7:50pm

Calculus
20^n = 5^n * 4^n so, you have 5^n/20^n + 4^n/20^n = 1/4^n + 1/5^n both of which converge
Thursday, April 3, 2014 at 7:44pm

Calculus
Determine whether the series is convergent or divergent. If it is convergent, find its sum. If it is divergent, enter NONE. sum from 1 to infinity of (5^n+4^n)/20^n It is convergent, but I do not know how to find the sum.
Thursday, April 3, 2014 at 1:15pm

Calculus
Determine whether the series is convergent or divergent. If it is convergent, find its sum. If it is divergent, enter NONE. sum from 1 to infinity of 1/e^2n. It is convergent, but I do not know how to solve for the sum.
Thursday, April 3, 2014 at 1:13pm

Calculus 12 Optimization
43
Thursday, April 3, 2014 at 7:19am

calculus
I have this question in my homework .its a multiple choice, Select the correct answer. Answers are in billions of dollars per year. and the answers are a)137.4 b)44.4 c)22.2 d)16.96 e)27.48
Thursday, April 3, 2014 at 4:02am

Calculus
dy/dx
Thursday, April 3, 2014 at 12:28am

calculus
dg
Wednesday, April 2, 2014 at 10:10pm

Calculus
If y = y(x), write y’ in Leibniz notation.
Wednesday, April 2, 2014 at 10:00pm

calculus
let the two equal width be x let the single side by y xy = 600 y = 600/x cost = 20y + 30x = 20(600/x) + 30x d(cost)/dx = -12000/x^2 + 30 = 0 for a min of cost 30 = 12000/x^2 x^2 = 400 x = 20 the two equal sides are 20 yds each, and the long side is 600/20 = 30 yds.
Wednesday, April 2, 2014 at 8:49pm

calculus
revenue function of x^2+3p=675
Wednesday, April 2, 2014 at 8:37pm

calculus
a farmer wishes to fence off a rectangular plot of land, using an existing wall as one of the sides . the total are enclosed must be 600 square yards. the fence on the side parallel to the wall will cost 20$ per yard, while the fences on the other side will cost 30$ per yard. ...
Wednesday, April 2, 2014 at 8:36pm

Calculus
g'(x)=af'(x). Try to prove this using the definition of the derivative.
Wednesday, April 2, 2014 at 8:29pm

Calculus
If g(x) = a f(x); find g’(x). Is it g'(x)=af?
Wednesday, April 2, 2014 at 8:13pm

calculus
I see that C(1990) is given as 271.9 What are you asking?
Wednesday, April 2, 2014 at 7:27pm

Calculus Help Please!!! Check
looks like you are using Newton's Formula for Cooling properly.
Wednesday, April 2, 2014 at 7:14pm

calculus
Let C(t) be the total value of US currency (coins and banknotes) in circulation at time. The table gives values of this function from 1980 to 2000, as of September 30, in billions of dollars. Estimate the value of C(1990) . t 1980 1985 1990 1995 2000 C(t) 129.9 187.3 271.9 409...
Wednesday, April 2, 2014 at 6:59pm

Calculus Help Please
the linear app. appears to be best for the function ___f___ since it is closer to ___f__ for a larger domain than it is to _g and h____ . the app. looks worst for ___h__ since _h____ moves away from L faster than __f and g___ do.
Wednesday, April 2, 2014 at 6:58pm

Calculus Help Please Check!!!
Lf(x)= 1-2x Lg(x)= 1-2x Lh(x)= 1-2x the linear app. appears to be best for the function ___f___ since it is closer to _____ for a larger domain than it is to _____ . the app. looks worst for ___h__ since _____ moves away from L faster than _____ do. i couldn't figure out ...
Wednesday, April 2, 2014 at 6:27pm

Calculus Help Please!!!
I got the answer. It is 4 % increases in blood flow. thanks anyway.
Wednesday, April 2, 2014 at 6:08pm

Calculus Help Please!!! Check
When a cold drink is taken from a refrigerator, its temperature is 5°C. After 25 minutes in a 20°C room its temperature has increased to 10°C. (Round the answers to two decimal place.) (a) What is the temperature of the drink after 60 minutes? (b) When will its ...
Wednesday, April 2, 2014 at 6:00pm

Calculus Help Please
let f(x)=(x-1)^2, g(x)=e^(-2x), and h(x)=1+ ln(1-2x) find linearization of f, g, and h at a=0 Lf(x)= Lg(x)= Lh(x)= graph f,g, and h, and their linear app. For which function is the linear app. best? for which is the worst? explain. the linear app. appears to be best for the ...
Wednesday, April 2, 2014 at 5:28pm

Calculus Help Please!!!
When blood flows along a blood vessel, the flux F (the volume of blood per unit time that flows past a given point) is proportional to the fourth power of the radius R of the blood vessel: F = kR4 (This is known as Poiseuille's Law.) A partially clogged artery can be ...
Wednesday, April 2, 2014 at 5:22pm

Calculus Help
I can add more rats!! last step: dx/dt = -6( csc^2 (π/3)) (-π/3) = -6((4/3)(-π/3) = 24π/9 km/min = 8π/3 km/min (which is Steve's answer)
Wednesday, April 2, 2014 at 5:10pm

Calculus Help
At a time of t min after the plane passed over the tracking telescope, let the horizontal distance be x km Let the angle of elevation be Ø Make a sketch, I get cot Ø = x/6 x = 6cotØ dx/dt = -6 csc^2 Ø dØ/dt when Ø = π/3 and d&...
Wednesday, April 2, 2014 at 5:06pm

Calculus - oops
rats - that's dx/dt = -6csc^2θ dθ/dt when θ=π/3, we have x = 6/√3 and cscθ = 2/√ dx/dt = -6(4/3)(-π/3) = 8π/3 km/min
Wednesday, April 2, 2014 at 5:02pm

Calculus Help
At t=0, let x=0, so that at time t, x/6 = cotθ x = 6cotθ dx/dt = -6sec^2θ dθ/dt when θ=π/3, we have x = 6/√3 and secθ = 2 dx/dt = -6(2)(-π/3) = 4π km/min
Wednesday, April 2, 2014 at 5:00pm

Calculus Help Please!!! Check
Odd notation. P is a point (x,y) so usually we would see dy/dx = 3y y = c*e^3x 2 = c, so y = 2e^(3x) You divided the right side by 3 and multiplied the left aside by 3, but that was not correct: dy/dp = 3y ∫dy/y = ∫3dp ...
Wednesday, April 2, 2014 at 4:50pm

Calculus Help
A plane flies horizontally at an altitude of 6 km and passes directly over a tracking telescope on the ground. When the angle of elevation is π/3, this angle is decreasing at a rate of π/3 rad/min. How fast is the plane traveling at that time?
Wednesday, April 2, 2014 at 4:47pm

calculus help thanks!
PV = nRT V dP/dt + P dV/dt = nR dT/dt Now just plug in the data: (14)(0.13) + (8.0)(-0.17) = (10)(0.0821) dT/dt dT/dt = 0.56 °K/s
Wednesday, April 2, 2014 at 4:45pm

Calculus Help Please!!!
When a cold drink is taken from a refrigerator, its temperature is 5°C. After 25 minutes in a 20°C room its temperature has increased to 10°C. (Round the answers to two decimal place.) (a) What is the temperature of the drink after 60 minutes? (b) When will its ...
Wednesday, April 2, 2014 at 4:43pm

Calculus Help Please!!! Check
A curve passes through the point (0, 2) and has the property that the slope of the curve at every point P is three times the y-coordinate of P. Find an equation of the curve. dy/dp = 3y or ∫ (3/y) dy = ∫ dp or 3 ln(y) = p + c or @ (0,2) ln(2) = 0 + c or c = ln(2) 3...
Wednesday, April 2, 2014 at 4:39pm

Calculus Help Please!!!
given : dr/dt = 40 cm/s A = πr^2 dA/dt = 2π r dr/dt case 1: when s = 1, r = 40 dA/dt = 2π(40)(40) = 3200π cm^2/sec case 2: when s = 3, r = 3(4) = 120 cm dA/dt = 2π(120)(40) = 9600π cm^2/sec case 3: ... your turn .....
Wednesday, April 2, 2014 at 4:37pm

calculus help thanks!
The gas law for an ideal gas at absolute temperature T (in kelvins), pressure P (in atmospheres), and volume V (in liters) is PV = nRT, where n is the number of moles of the gas and R = 0.0821 is the gas constant. Suppose that, at a certain instant, P = 8.0 atm and is ...
Wednesday, April 2, 2014 at 4:35pm

Calculus Help Please!!!
A stone is dropped into a lake, creating a circular ripple that travels outward at a speed of 40 cm/s. Find the rate at which the area within the circle is increasing after each of the following. after 1 s = after 3 s = after 7 s =
Wednesday, April 2, 2014 at 4:32pm

Calculus Help Please!!!
f(x) is differentiable on the interval. So, you know there is a c such that f'(c) = (f(2)-f(0)/(2-0) = (-1-2)/2 = -3/2 So, just solve for c in 4c-5 = -3/2 c = 7/8 as a check, view http://www.wolframalpha.com/input/?i=plo​t+y+%3D+2x^2-5x%2B1+and+y+%3D+%28-3%2F2%​...
Tuesday, April 1, 2014 at 11:46pm

Calculus Help Please!!!
well, f(x) is only defined on 0 <= x <= 1 Visit http://rechneronline.de/function-graphs/​ and enter 8x*sqr(x-x^2) for your function. Set the range of y to be 2.5 to 3 and the peak will be quite clear
Tuesday, April 1, 2014 at 11:40pm

Calculus Help Please!!!
Consider the following. f(x) = 8x (square root of (x − x^2)) (a) Use a graph to find the absolute maximum and minimum values of the function to two decimal places.
Tuesday, April 1, 2014 at 10:27pm

Calculus Help Please!!!
Does the function satisfy the hypotheses of the Mean Value Theorem on the given interval? f(x) = 2x^2 − 5x + 1, [0, 2] If it satisfies the hypotheses, find all numbers c that satisfy the conclusion of the Mean Value Theorem. (Enter your answers as a comma-separated list...
Tuesday, April 1, 2014 at 10:08pm

Calculus Help Please!!!
done http://www.jiskha.com/display.cgi?id=139​6400942 are you switching names???
Tuesday, April 1, 2014 at 9:42pm

Calculus Help Please!!!
Use the product rule to get f ' (t) = -(t^2 - 32)/√(64-t^2) = 0 for a local max/min t^2 = 32 t = ±4√2 f(±4√2) = 0 f(-1) = -1√63 f(8) = 8(√0) = 0 there you go, you got your f(t)'s what do you think? Here is your graph, notice ...
Tuesday, April 1, 2014 at 9:41pm

Calculus Help!
see http://www.jiskha.com/display.cgi?id=139​6388805
Tuesday, April 1, 2014 at 9:27pm

Calculus Help Please!!!
Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = xe^((−x^2)/98), [−6, 14]
Tuesday, April 1, 2014 at 9:14pm

Calculus Help Please!!!
Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = (t square root of (64 − t^2)) ,[−1,8]
Tuesday, April 1, 2014 at 9:11pm

Calculus Help!
Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = xe^(−x^(2)/98), [−6, 14]
Tuesday, April 1, 2014 at 9:09pm

calculus
5x^2
Tuesday, April 1, 2014 at 8:19pm

Calculus Help Please!!!
looks like we both messed up in the f(x) calculations should be f(4) = 2(64) - 3(16) - 72(4) + 7 = -201 f(-3) = 2(-27) - 3(9) - 72(-3)+7 = 142 end-values: f(-4) = 2(-64) - 3(16)( - 72(-4) + 7 = 119 f(5) = 2(125) - 3(25) - 72(5) + 7 = -178
Tuesday, April 1, 2014 at 6:34pm

Calculus
f ' (t) = -8sin t + 2(4 cos t) = -8sint + 8cost = 0 for a max/min 8sint = 8cost sint/cost = 1 tant = 1 t = 45° or 225° or t = π/4 , t = 5π/4 -->(outside our domain) so evaluate f(0) f(π/4) f(π/2) and determine which is the largest and which ...
Tuesday, April 1, 2014 at 6:24pm

Calculus Help Please!!!
so it the same way you were just given in your previous post. Let us know what you got
Tuesday, April 1, 2014 at 6:07pm

Calculus Help Please!!!
f ' (x) = 6x^2 - 6x - 72 = 0 for a local max/min x^2 - x - 12 = 0 (x-4)(x+3) = 0 x = 4, or x = -3 f(4) = 2(64) - 3(16) - 72(4) + 7 = -201 f(-3) = 2(-27) - 3(9) - 72(-3)+7 = 115 end-values: f(-4) = 2(-64) - 2(16)( - 72(-4) + 7 = 135 f(5) = 2(125) - 3(25) - 72(5) + 7 = -178 ...
Tuesday, April 1, 2014 at 6:04pm

Calculus Help Please!!!
f'(x) = 6x^2 -6x -72 f'(0) = 6(x^2 -x-12) 0 = 6(x+ 3) (x-4) x = -3, 4 f(-4) = 2(-4)^3 -3(-4)^2 -72(-4) +7= 139 f(-3) = 2(-3)^3 -3(-3)^2 -72(-3) +7=132 f(4) = 2(4)^3 -3(4)^2 -72(4) + 7= -145 f(5) = 2(5)^3 -3(5)^2 -72(5)+7= -178
Tuesday, April 1, 2014 at 6:01pm

Calculus
Find the absolute minimum and absolute maximum values of f on the given interval. f(t) = 8 cos t + 4 sin 2t, [0, π/2]
Tuesday, April 1, 2014 at 5:45pm

Calculus Help Please!!!
Find the absolute maximum and absolute minimum values of f on the given interval. f(t) = (t square root of (64 − t^2)), [−1, 8]
Tuesday, April 1, 2014 at 5:27pm

Calculus Help Please!!!
Find the absolute maximum and absolute minimum values of f on the given interval. f(x) = 2x^3 − 3x^2 − 72x + 7 , [−4, 5]
Tuesday, April 1, 2014 at 5:26pm

calculus and vectors
Add the 2 equations ... 6x + y = 6 y = 6-6x let x = 0 , y = 6 2(0) + 4(6) + z = 5 --> z = -19) we have a point (0,6,-19) on the line of intersection let x = 1, y = 0 2(1) + 4(0) + z = 5 --> z = 3 and (1,0,3) is another point on that line So a direction vector of that ...
Tuesday, April 1, 2014 at 5:18pm

calculus and vectors
Determine an equation of the line of intersection of the planes 4x − 3y − z = 1 and 2x + 4y + z = 5.
Tuesday, April 1, 2014 at 4:59pm

calculus
max area for a given perimeter is a circle. Is the wire evenly divided? If so, c = p/2, so r = p/4π, and the total area is a = 2(πr^2) = 2π(p^2/16π^2) = p^2/8π If not, then if we have a tiny circle, (area effectively zero), then r = p/2π and a...
Tuesday, April 1, 2014 at 12:30pm

calculus
Twenty feet wire is used to make two figures? What is the maximum areas of enclosed figures.
Tuesday, April 1, 2014 at 11:14am

Calculus
Thanks Mr. Steve for the guidance.
Tuesday, April 1, 2014 at 5:21am

Calculus
Looks good to me. I get ∫[1,2] (3-x) - 2/x dx = 3x - 1/2 x^2 - 2logx [1,2] = 3/2 - 2log2 gotta be a typo in the answer. 2log2 is correct.
Tuesday, April 1, 2014 at 4:52am

Calculus
Find the area cut off by x+y=3 from xy=2. I have proceeded as under: y=x/2. Substituting this value we get x+x/2=3 Or x+x/2-3=0 Or x^2-3x+2=0 Or (x-1)(x-2)=0, hence x=1 and x=2 are the points of intersection of the curve xy=2 and the line x+y=3. Area under curve above X axis ...
Tuesday, April 1, 2014 at 3:07am

Calculus
Good idea. However, in an attempt to use your math, and also to apply to a possibly more general problem later, try implicit differentiation: x^2 + y^2 = 18 2x + 2yy' = 0 y' = -x/y So, if -x/y = 1 and x^2+y^2 = 18, 2x^2 = 18 x = ±3 Now, figuring y should not be ...
Monday, March 31, 2014 at 1:02pm

Calculus
LOL, sketch a graph !
Monday, March 31, 2014 at 11:46am

Calculus
The circle defined by the equation x^2 + y^2 = 18 has two points where the slope of its tangent line is m=1. Find those points.
Monday, March 31, 2014 at 11:41am

Calculus: Integral
recall that sec^2 = 1+tan^2, so you have ∫sec^4(4x) dx = ∫sec^2(4x)(1 + tan^2(4x)) dx = ∫sec^2(4x) dx + ∫tan^2(4x) sec^2(4x) dx = 1/4 tan(4x) + (1/4)(1/3) tan^3(4x) and you can massage that in several ways.
Monday, March 31, 2014 at 5:32am

Calculus: Integral
I don't understand how to do this one integral problem that involves secant. I'm asked to find the integral of sec^4 (4x). I'm not really sure how to go about solving this problem.
Monday, March 31, 2014 at 3:32am

Calculus Help Please!!!
looking at a diagram, if A is a away from Q and B is b away from Q, then √(a^2+144) + √(b^2+144) = 39 a/√(a^2+144) da/dt + b/√(b^2+144) db/dt = 0 Now just plug in da/dt = 3.5 a = 5 b = 23.065 (from 1st equation when a=5) and solve for db/dt
Monday, March 31, 2014 at 12:27am

Calculus Help
v = 2/3 pi r^3 (half a sphere) dv = 2 pi r^2 dr now just plug in the given r and dr watch the units.
Monday, March 31, 2014 at 12:07am

Calculus Help Please!!!
v = 4/3 pi r^3 dv = 4 pi r^2 dr c = 2pi r dc = 2pi dr so, dr = dc/(2pi) meaning that dv = 4 pi r^2 dc/(2pi) = 2 r^2 dr so, using the given numbers, dv = 2*(80/2pi)^2 * 0.5 = 1600/pi^2
Monday, March 31, 2014 at 12:05am

Calculus Help Please!!!
looks good to me
Monday, March 31, 2014 at 12:01am

pre calculus
24
Sunday, March 30, 2014 at 11:40pm

Calculus Help Please!!!
Verify the given linear approximation at a = 0. Then determine the values of x for which the linear approximation is accurate to within 0.1. (Enter your answer using interval notation. Round your answers to three decimal places.) fourth root of (1 + 2x)≈ 1 + (1/2)x
Sunday, March 30, 2014 at 11:21pm

Calculus Help Please!!!
The circumference of a sphere was measured to be 80 cm with a possible error of 0.5 cm. 1) Use differentials to estimate the maximum error in the calculated volume. (Round your answer to the nearest integer.) 2) What is the relative error? (Round your answer to three decimal ...
Sunday, March 30, 2014 at 11:17pm

Calculus Help
Use differentials to estimate the amount of paint needed to apply a coat of paint 0.03 cm thick to a hemispherical dome with diameter 54 m. (Round your answer to two decimal places.)
Sunday, March 30, 2014 at 11:16pm

Calculus Help Please
f(x) = f(a) + (x-a) f'(a) f(x) = x^4 df/dx = 4x^3 let a = 2 then f(a) = 2^4 = 16 f'(a) = 4*8 = 32 f(x) = 16 + (x-a)(32) x-a = - .001 so f(1.999) = 16 -.001(32) = 16 - .032 f(1.999) = 15.968 with calculator it is 15.968 also
Sunday, March 30, 2014 at 10:29pm

Calculus Help Please!!!
at x = 3 y = 3*3 - 9 = 0 at x = 2.4 y = 3(2.4) - 2.4^2 = 1.44 delta y = 1.44 -0 = 1.44 dy/dx = 3 - 2 x at x = 3 dy/dx = 3 - 6 = -3 if dx = -.6 dy = -3 (-.6) = 1.8
Sunday, March 30, 2014 at 10:21pm

Calculus
Thanks Damon, that really clears it up for me
Sunday, March 30, 2014 at 10:17pm

Calculus Help Please
Use a linear approximation (or differentials) to estimate the given number. (1.999)^4
Sunday, March 30, 2014 at 10:14pm

Calculus Help Please!!!
Oh, I see f(x) = ln (1+x) df/dx = 1/(1+x) d^2f/dx^2 = -1/(1+x)^2 f(x) = f(0) + [1/(1+0)] x - x^2/2! ... f(x) = 0 + x - x^2/2 + ..... well at a first cut when is x^2/2 =.1 x? x/2 = .1 x = .2
Sunday, March 30, 2014 at 10:13pm

Calculus Help Please!!!
Compute Δy and dy for the given values of x and dx = Δx. (Round your answers to three decimal places.) y = 3x − x^2, x = 3, Δx = −0.6 Δy=???
Sunday, March 30, 2014 at 9:57pm

Calculus Help Please!!!
Verify the given linear approximation at a = 0. Then determine the values of x for which the linear approximation is accurate to within 0.1. (Enter your answer using interval notation. Round your answers to three decimal places.) ln(1 + x) ≈ x xE
Sunday, March 30, 2014 at 8:28pm

Calculus Help Please!!!
Two carts, A and B, are connected by a rope 39 ft long that passes over a pulley P (see the figure). The point Q is on the floor h = 12 ft directly beneath P and between the carts. Cart A is being pulled away from Q at a speed of 3.5 ft/s. How fast is cart B moving toward Q at...
Sunday, March 30, 2014 at 7:16pm

Calculus Help Please!!!
LOL - Guess which of us is the mathematician and which is the Engineer :)
Sunday, March 30, 2014 at 7:15pm

Calculus Help Please!!!
when the water has depth x, the cross-section is a trapezoid with bases 30 and 30+x. So the volume of water at depth x is v = (60+x)/2 * x * 500 cm^3 = 250x^2 + 15000x so, knowing that dv/dt = (500x + 15000) dx/dt just solve that for dx/dt when x=20
Sunday, March 30, 2014 at 7:12pm

Calculus Help Please!!!
Q = incoming flow rate = .1 m^3/min dh/ dt = Q A where A = surface area = length * width at 20 cm depth which depth is (1/2) height width = 30 + 1/2(70-30) = 30+20 = 50 cm = .5 m wide water surface so A = 5 * .50 =2.5 m^3 so finally dh/dt = .1 * 2.5 = .25 m/min = 25 cm/min
Sunday, March 30, 2014 at 7:11pm

Calculus Help Please!!!
A water trough is 5 m long and has a cross-section in the shape of an isosceles trapezoid that is 30 cm wide at the bottom, 70 cm wide at the top, and has height 40 cm. If the trough is being filled with water at the rate of 0.1 m3/min how fast is the water level rising when ...
Sunday, March 30, 2014 at 6:43pm

physics
find the difference in PE in the two locations. Hold one charge stationary. PEtotal= kQQ/.1 PE(new total)=KQQ/.06 subtract the first from the second, that must equal the work done. There are more difficult ways to work this, involving finding work in an integral calculus ...
Sunday, March 30, 2014 at 10:11am

Calculus
when dy/du = u^½ what does y = ? Just a simple power rule substitution. dy/du = u^n y = u^(n+1) / (n+1) + C
Saturday, March 29, 2014 at 4:38pm

Calculus
Thanks Steve! Finally got this one correct on Math Lab! I am eternally grateful, and have made an account here so I can get help and I have already tried helping others as well. I am very pleased with the service of this site and am glad to have found it :) Hooray!!!
Saturday, March 29, 2014 at 4:34pm

Calculus
When dy/dx=(x-6)^½ what does y equal?
Saturday, March 29, 2014 at 4:11pm

Calculus
the rate of change of volume is the surface area times the rate of change of height 450 ft^3/min = surface area * dh/dt surface area = pi r^2 450 = pi (30^2) dh/dt dh/dt = .159 ft/min You could do this by saying V = pi r^2 h dV/dh = pi r^2 dV/dh*dh/dt = pi r^2 dh/dt chain rule...
Friday, March 28, 2014 at 11:48pm

Calculus
Jesse has constructed a huge cylindrical can with a diameter of 60 ft. The can is being filled with water at a rate of 450 ft3/min. How fast is the depth of the water increasing? (Hint: The volume of water in the cylinder is determined by πr2h where r is the radius and h ...
Friday, March 28, 2014 at 11:39pm

math
assume no calculus allowed thus complete he square to find the vertex of this parabola 16 t^2 - 20 t - 2 = -h 16 t^2 -20 t = - h + 2 t^2 - 5/4 t = - h/16 + 1/8 t^2- 5/4 t+ 25/64 = -h/16 + 8/64 + 25/64 (t - 5/8)^2 = -(1/16)(h - 33/4) so in 5/8 of a second it reaches the vertex ...
Friday, March 28, 2014 at 10:37pm

Calculus
so it is positive for x>.316 and for x <.316
Friday, March 28, 2014 at 8:12pm

Calculus
Note that you did the second derivative correctly. It is easier to write it their way y" = 10e^(-5x^2)(10x^2-1) It is zero at x = +/- .316
Friday, March 28, 2014 at 8:11pm

Calculus
first http://www.wolframalpha.com/input/?i=plo​t++e^%28-5x^2%29 Then this for second derivative and graph https://www.wolframalpha.com/input/?i=se​cond+derivative+of+e^%28-5x^2%29
Friday, March 28, 2014 at 7:57pm

Calculus
first http://www.wolframalpha.com/input/?i=plo​t++e^%28-5x^2%29
Friday, March 28, 2014 at 7:52pm

Calculus
At what interval is e^(-5x^2) concave up? I know the second derivative is 100x^2*e^-5x^2-10*e^-5x^2 but I just can not figure this one out. Thank you for your help!
Friday, March 28, 2014 at 7:38pm

Calculus
Thanks for the advice. I checked the problem statment and answer several times and got the same result. I also suspect it to be a print mistake in the book.
Friday, March 28, 2014 at 7:46am

Calculus
As a first check, I went to http://www.wolframalpha.com/input/?i=2%E​2%88%AB[3%2C4]+%282%2F3+%E2%88%9A%28x^2-​9%29%29+dx and saw that they show the area as 2.28 So, I suspect there is an error in the problem or the answer. Your calculation appears to be correct, ...
Friday, March 28, 2014 at 5:43am

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