Math 1425.P70 Test 1 Name _____________________________________________ 9/18/2014
Use the graph to evaluate the limit.1)
x-5 -4 -3 -2 -1 1 2 3 4 5
y4321
-1-2-3-4
x-5 -4 -3 -2 -1 1 2 3 4 5
y4321
-1-2-3-4
limx→0
f(x)
2) limx→0
f(x)
x-8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9
y
1
-1
x-8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9
y
1
-1
Find the limit, if it exists.
3) limx→3
x2 + 8x + 16
Test 1
Find a simplified difference quotient for the function.
4) f(x) = 10x
Find the limit, if it exists.
5) limx → 7
x2 + 3x - 70x2 - 49
Math 1425.P70 Test 1, page A-2
Find the slope of the tangent line at the given value of the independent variable.
6) f(x) = 3x + 2x
, x = 8
Find the equation for the tangent to the curve at the given point.7) f(x) = x2 + 5x ; (4, 36)
Math 1425.P70 Test 1, page A-3
Find the second derivative.
8) s = 2t33
+ 2
Solve the problem.9) If s is a distance given by s(t) = 5t3 + 4t2 + 4t , find the acceleration, a(t).
Math 1425.P70 Test 1, page A-4
The function s = f(t) gives the position of a body moving on a coordinate line, with s in meters and t in seconds.10) s = 4t2 + 3t + 5, 0 ≤ t ≤ 2
Find the body's speed and acceleration at the end of the time interval.
Solve the problem.11) Find the points where the graph of the function has horizontal tangents.
f(x) = 3x2 + 5x + 2
Math 1425.P70 Test 1, page A-5
Answer KeyTestname: TEST1
1) Does not exist2) 13) 7
4) - 10x2 + xh
5) 1714
6) 9532
7) y = 13x - 168) 4t9) a(t) = 30t + 8
10) 19 m/sec, 8 m/sec2
11) - 56
, - 112
Math 1425.P70 Test 1, page A-6
Math 1425.P70 Test 1 Name _____________________________________________ 9/18/2014
Use the graph to evaluate the limit.1)
x-5 -4 -3 -2 -1 1 2 3 4 5
y4321
-1-2-3-4
x-5 -4 -3 -2 -1 1 2 3 4 5
y4321
-1-2-3-4
limx→0
f(x)
2) limx→0
f(x)
x-8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9
y
1
-1
x-8 -7 -6 -5 -4 -3 -2 -1 1 2 3 4 5 6 7 8 9
y
1
-1
Find the limit, if it exists.
3) limx→3
x2 + 10x + 25
Test 1
Find a simplified difference quotient for the function.
4) f(x) = 4x
Find the limit, if it exists.
5) limx → 3
x2 + 7x - 30x2 - 9
Math 1425.P70 Test 1, page B-2
Find the slope of the tangent line at the given value of the independent variable.
6) f(x) = 4x + 2x
, x = 6
Find the equation for the tangent to the curve at the given point.7) f(x) = x2 + 5x ; (4, 36)
Math 1425.P70 Test 1, page B-3
Find the second derivative.
8) s = 5t33
+ 5
Solve the problem.9) If s is a distance given by s(t) = 5t3 + 2t2 + 4t , find the acceleration, a(t).
Math 1425.P70 Test 1, page B-4
The function s = f(t) gives the position of a body moving on a coordinate line, with s in meters and t in seconds.10) s = 3t2 + 4t + 6, 0 ≤ t ≤ 2
Find the body's speed and acceleration at the end of the time interval.
Solve the problem.11) Find the points where the graph of the function has horizontal tangents.
f(x) = 3x2 + 7x - 5
Math 1425.P70 Test 1, page B-5
Answer KeyTestname: TEST1
1) Does not exist2) 13) 8
4) - 4x2 + xh
5) 136
6) 7118
7) y = 13x - 168) 10t9) a(t) = 30t + 4
10) 16 m/sec, 6 m/sec2
11) - 76
, - 10912
Math 1425.P70 Test 1, page B-6
