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Write an integral that quantifies the increase in the surface area of a sphere as its radius doubles from R unit to 2 R units and evaluate the integral.

12 π R 2 = 8 π R 2 R r d r

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Write an integral that quantifies the increase in the volume of a sphere as its radius doubles from R unit to 2 R units and evaluate the integral.

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Suppose that a particle moves along a straight line with velocity v ( t ) = 4 2 t , where 0 t 2 (in meters per second). Find the displacement at time t and the total distance traveled up to t = 2 .

d ( t ) = 0 t v ( s ) d s = 4 t t 2 . The total distance is d ( 2 ) = 4 m .

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Suppose that a particle moves along a straight line with velocity defined by v ( t ) = t 2 3 t 18 , where 0 t 6 (in meters per second). Find the displacement at time t and the total distance traveled up to t = 6 .

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Suppose that a particle moves along a straight line with velocity defined by v ( t ) = | 2 t 6 | , where 0 t 6 (in meters per second). Find the displacement at time t and the total distance traveled up to t = 6 .

d ( t ) = 0 t v ( s ) d s . For t < 3 , d ( t ) = 0 t ( 6 2 t ) d t = 6 t t 2 . For t > 3 , d ( t ) = d ( 3 ) + 3 t ( 2 t 6 ) d t = 9 + ( t 2 6 t ) . The total distance is d ( 6 ) = 9 m .

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Suppose that a particle moves along a straight line with acceleration defined by a ( t ) = t 3 , where 0 t 6 (in meters per second). Find the velocity and displacement at time t and the total distance traveled up to t = 6 if v ( 0 ) = 3 and d ( 0 ) = 0 .

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A ball is thrown upward from a height of 1.5 m at an initial speed of 40 m/sec. Acceleration resulting from gravity is −9.8 m/sec 2 . Neglecting air resistance, solve for the velocity v ( t ) and the height h ( t ) of the ball t seconds after it is thrown and before it returns to the ground.

v ( t ) = 40 9.8 t ; h ( t ) = 1.5 + 40 t 4.9 t 2 m/s

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A ball is thrown upward from a height of 3 m at an initial speed of 60 m/sec. Acceleration resulting from gravity is −9.8 m/sec 2 . Neglecting air resistance, solve for the velocity v ( t ) and the height h ( t ) of the ball t seconds after it is thrown and before it returns to the ground.

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The area A ( t ) of a circular shape is growing at a constant rate. If the area increases from 4 π units to 9 π units between times t = 2 and t = 3 , find the net change in the radius during that time.

The net increase is 1 unit.

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A spherical balloon is being inflated at a constant rate. If the volume of the balloon changes from 36 π in. 3 to 288 π in. 3 between time t = 30 and t = 60 seconds, find the net change in the radius of the balloon during that time.

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Water flows into a conical tank with cross-sectional area πx 2 at height x and volume π x 3 3 up to height x . If water flows into the tank at a rate of 1 m 3 /min, find the height of water in the tank after 5 min. Find the change in height between 5 min and 10 min.

At t = 5 , the height of water is x = ( 15 π ) 1 / 3 m . . The net change in height from t = 5 to t = 10 is ( 30 π ) 1 / 3 ( 15 π ) 1 / 3 m.

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A horizontal cylindrical tank has cross-sectional area A ( x ) = 4 ( 6 x x 2 ) m 2 at height x meters above the bottom when x 3 .

  1. The volume V between heights a and b is a b A ( x ) d x . Find the volume at heights between 2 m and 3 m.
  2. Suppose that oil is being pumped into the tank at a rate of 50 L/min. Using the chain rule, d x d t = d x d V d V d t , at how many meters per minute is the height of oil in the tank changing, expressed in terms of x , when the height is at x meters?
  3. How long does it take to fill the tank to 3 m starting from a fill level of 2 m?
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Questions & Answers

f(x) = x-2 g(x) = 3x + 5 fog(x)? f(x)/g(x)
Naufal Reply
fog(x)= f(g(x)) = x-2 = 3x+5-2 = 3x+3 f(x)/g(x)= x-2/3x+5
diron
pweding paturo nsa calculus?
jimmy
how to use fundamental theorem to solve exponential
JULIA Reply
find the bounded area of the parabola y^2=4x and y=16x
Omar Reply
what is absolute value means?
Geo Reply
Chicken nuggets
Hugh
🐔
MM
🐔🦃 nuggets
MM
(mathematics) For a complex number a+bi, the principal square root of the sum of the squares of its real and imaginary parts, √a2+b2 . Denoted by | |. The absolute value |x| of a real number x is √x2 , which is equal to x if x is non-negative, and −x if x is negative.
Ismael
find integration of loge x
Game Reply
find the volume of a solid about the y-axis, x=0, x=1, y=0, y=7+x^3
Godwin Reply
how does this work
Brad Reply
Can calculus give the answers as same as other methods give in basic classes while solving the numericals?
Cosmos Reply
log tan (x/4+x/2)
Rohan
please answer
Rohan
y=(x^2 + 3x).(eipix)
Claudia
is this a answer
Ismael
A Function F(X)=Sinx+cosx is odd or even?
WIZARD Reply
neither
David
Neither
Lovuyiso
f(x)=1/1+x^2 |=[-3,1]
Yuliana Reply
apa itu?
fauzi
determine the area of the region enclosed by x²+y=1,2x-y+4=0
Gerald Reply
Hi
MP
Hi too
Vic
hello please anyone with calculus PDF should share
Adegoke
Which kind of pdf do you want bro?
Aftab
hi
Abdul
can I get calculus in pdf
Abdul
explain for me
Usman
okay I have such documents
Fitzgerald
please share it
Hamza
How to use it to slove fraction
Tricia Reply
Hello please can someone tell me the meaning of this group all about, yes I know is calculus group but yet nothing is showing up
Shodipo
You have downloaded the aplication Calculus Volume 1, tackling about lessons for (mostly) college freshmen, Calculus 1: Differential, and this group I think aims to let concerns and questions from students who want to clarify something about the subject. Well, this is what I guess so.
Jean
Im not in college but this will still help
nothing
how en where can u apply it
Migos
how can we scatch a parabola graph
Dever Reply
Ok
Endalkachew
how can I solve differentiation?
Sir Reply
with the help of different formulas and Rules. we use formulas according to given condition or according to questions
CALCULUS
For example any questions...
CALCULUS
v=(x,y) وu=(x,y ) ∂u/∂x* ∂x/∂u +∂v/∂x*∂x/∂v=1
log tan (x/4+x/2)
Rohan
what is the procedures in solving number 1?
Vier Reply
Practice Key Terms 1

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Source:  OpenStax, Calculus volume 1. OpenStax CNX. Feb 05, 2016 Download for free at http://cnx.org/content/col11964/1.2
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