Limit Evaluation
Using direct substitution, evaluate the following integral. lim (2x2+4x-1)
x->3
Find the area bounded by the curve of the square of a variable, the horizontal axis, and the vertical lines where the variable equals one and four.
21
Find the average value of the function f(x)=3x2+2x over the interval [1,3]
17
Find the slope at the given point on the equation (f(x) = 2x2 - 5x + 1) at (x = 2)
3
Find the absolute maximum and minimum values of f(x)= 2x3-15x2+36x
Absolute maximum is 28
Absolute minimum is 27
Evaluate the following limit evaluation
lim (x2-4/x-2)
x->2
4
Evaluate the total accumulated value of the product of a variable and the square root of the quantity one plus the square of that variable, as it ranges from zero to the square root of three.
7/3
Find the average value of f(x)=5 over the interval [2,6]
5
Find the equation of the tangent line to the curve y= x3 at the point (2,8)
y-8=12(x-2) or y=12x-16
Find x values where there is an absolute maximum and minimum values of f(x)=x4-4x3 on the interval [-1,4]
Absolute maximum at x=-1
Absolute minimum at x=3
Solve the following limit evaluation
lim [(√x)-2/x-4]
x->4
1/4
Determine the net area under the curve of the sine of a variable over one full positive half-cycle, starting from zero and ending at pi.
2
Find the average value of f(x)=x over the interval [0,4]
2
Find the slope of the tangent line to the circle x2+y2=25 at the point (3,4)
-3/4
Find the absolute maximum and minimum values of f(x)=sin(x)+cos(x) on the interval [0,π] (Yes that is pie)
Absolute maximum is √2
Absolute minimum is -1
Evaluate
lim (3x2+5/2x2-x
x-> ∞
3/2
Accumulate the rate of growth described by the constant e raised to the power of three times a variable, as the variable increases from zero to two.
1/3(e6-1)
Find the average value of f(x)=3x2 over the interval [0,2]
4
Find the slope of the tangent line to f(x)=1/x at x=1
0
Find the absolute maximum and minimum values of f(x)=(x/x2+1) on the interval [0,3]
Absolute maximum is at 0.5
Absolute minimum is at 0
Evaluate the following (The 3x is included in the radical (√4x2+3x/2x-5)
x->∞
Integrate the multiplicative inverse of a variable plus two, over the interval where the variable goes from negative one to three.
ln(5)
During a 9-hour workday, the production rate of a factory t hours after the start of the shift is given by the function r(t)=5+3t items per hour. Find the average hourly production rate.
18.5
Find the equation of the line tangent to the curve y= x2+3x at the point where x=2
y=7x-4
Find the absolute maximum and minimum values for f(x)=x2/3 on the interval (-1,8)
Absolute maximum is 4
Absolute minimum is 0