Show:
Limits
Derivatives
Integrals
Volume/Area
History of Calc/ MIsc
100
There is no b for which limx→c f(x) = b
What is the limit does not exist
100
If h(x) = 2x^2 + 1, find the slope of the tangent line at the point P(1, 3).
4
100
find ∫5dx from 0 to 4
20
100
Method of which the shape of a circle with a hole in it to help us find the volume of a shape created by rotating two functions around an axis.
washer method
100
The inventor of calculus
Who is Isaac Newton
200
f(x) = {x^3-4 for x<2 {2x for x>=2 What is the limit as x approaches 2 for f(x)?
both the limit from the right and the left equal 4 so the limit exists and is equal to 4
200
Find the derivative of y = 5x3 - √2x2 + 6x
15x2 - 2√2x + 6.
200
Evaluate the following. pi ∫ (sin x+2)dx 0
2pi + 2
200
This formula is used to find areas with more than one curve.
What is ∫a^b(f(x)-g(x) )dx
200
The other inventor of calculus
Who is Gottfried Wilhelm von Leibniz
300
Name 3 of the rules to find limits
What is Difference Rule, Constant Multiple Rule, Product Rule, Power Rule, Quotient Rule
300
What is the general formula for derivatives?
lim f(x+h)−f(x)/h as h approaches 0
300
Name 3 applications of integrals
Area under a curve, Total distance/displacement, Accumulation over time, Average Function Value , Area Between Two Curves, Volumes of Solids of Revolution / Method of Rings, Volumes of Solids of Revolution / Method of Cylinders
300
Find the integral ∫5x^2+3dx from 0 to 4
118.667
300
A function fails to be differentiable if it has a....
What is a discontinuity, corner, cusp or a vertical tangent
400
Name the 4 types of Discountinuties
What is Hole, Jump, Infinity, Oscillating
400
find the derivative of y=√13x^2-5x+8)
(26x-5)/(2√13x^2-5x+8)
400
This equation's derivative is: 25x^3 - 12x^2 + X. Find its intergral
What is the derivative of 25x^4/4 - 4x^3 + x^2/2?
400
Approximate the area under the curve f (x)=x^2+2, -2≤x≤ 1 with a Riemann sum, using six sub-intervals and right endpoints.
8.375
400
The inventor of calculus whose applications for calculus were geometrical and related to the physical world - such as describing the orbit of the planets around the sun. (one of the previous 2)
Who is Isaac Newton
500
Answer the following Limit Question: Lim sinx/x as x approaches 0
1
500
Determine all the numbers c which satisfy the conclusions of the Mean Value Theorem for the following function. f(x)=x^3+2x^2-x on [-1,2]
c= 0.7863
500
Integrate ∫(-1)^(3) ((2x+1)^2)dx.
57 1/3
500
Find the volume of the solid rotated about the line y= -2 for the region bounded by y=√ x+2) and y=e^2
19.724
500
Name 3 jobs that involve calculus
engineers, scientists, economists Credit card companies use calculus to set the minimum payments due on credit card statements at the exact time the statement is processed by considering multiple variables such as changing interest rates and a fluctuating available balance. Biologists use differential calculus to determine the exact rate of growth in a bacterial culture when different variables such as temperature and food source are changed. This research can help increase the rate of growth of necessary bacteria, or decrease the rate of growth for harmful and potentially threatening bacteria. An electrical engineer uses integration to determine the exact length of power cable needed to connect two substations that are miles apart. Because the cable is hung from poles, it is constantly curving. Calculus allows a precise figure to be determined. An architect will use integration to determine the amount of materials necessary to construct a curved dome over a new sports arena, as well as calculate the weight of that dome and determine the type of support structure required. Space flight engineers frequently use calculus when planning lengthy missions. To launch an exploratory probe, they must consider the different orbiting velocities of the Earth and the planet the probe is targeted for, as well as other gravitational influences like the sun and the moon. Calculus allows each of those variables to be accurately taken into account. Statisticians will use calculus to evaluate survey data to help develop business plans for different companies. Because a survey involves many different questions with a range of possible answers, calculus allows a more accurate prediction for appropriate action. A physicist uses calculus to find the center of mass of a sports utility vehicle to design appropriate safety features that must adhere to federal specifications on different road surfaces and at different speeds. An operations research analyst will use calculus when observing different processes at a manufacturing corporation. By considering the value of different variables, they can help a company improve operating efficiency, increase production, and raise profits. A graphics artist uses calculus to determine how different three-dimensional models will behave when subjected to rapidly changing conditions. This can create a realistic environment for movies or video games. and many more :)