Search & Filtering
Find the values of a and b that make f continuous everywhere.
f{x]= [(x^2+6x+5)/(x^2-3x-4)] , x < -1
(ax^2 - bx+ 3) , -1 less than equal to x < 3
2x - a + b , x Greater than equal to 3 .
A billiard ball is hit and travels in a straight line. If 𝑠 𝑐𝑚 is the distance of the ball from
its initial position at 𝑡 𝑠𝑒𝑐, then 𝑠 = 100𝑡2 + 100𝑡. If the ball hits the cushion that is 39 𝑐𝑚 from its
initial position, at what velocity does it hit the cushion?
A cable hangs in a parabolic arc between two poles 100 feet apart. The poles are 30 feet high and the lowest point on a suspended cable is 5 feet above the ground
a) find the equation of the arc if the vertex is the lowest points of the cable
b) find the height of the cable at a point 10 feet from one of the poles
The graph of the parametric equations is called a cycloid.
x=θ-sinθ and y=1-cosθ for 0≤θ≤2π
(a) find dy/dx
(b) find an equation of the tangent to the cycloid at the point where θ=π/3
(c) at what point is the tangent horizontal?
(d) graph the cycloid and the tangent lines in parts (b) and (c)
In numbers 5-7,
(a) make a table of values of t, x and y based on the specified intervals of the given parametic equations
(b) sketch the plane curve defined by the given parametic equations at the specified interval
(c) find dy/dx without eliminating the parameter t. simplify your answers
(d) find an equation such that the parameter t is eliminated
5. x=t²+1 and y=t³-2 for 0≤t≤2
6. x=sqrt(5t) and y=2t+2 for 0≤t≤5
7. x=cost and y=2-cos²t for 0≤t≤π
In numbers 1-4,
(a) find the critical numbers of the given functions
(b) using either the First or Second Derivative Test, classify whether thd function has a relative maximum or minimum at these critical numbers
(c) find the coordinates of the exterum points
(d) find the points of jnflection
(e) find the x and y - intercepts
(f) summarize the points in a table. include additional points necessary for the graph
(g) sketch the polunomial curves in graphic papers
1. f(x)=x³+x²-x+2
2. f(x)=(x4/4)-(x³/3)-2x²+4x+3
3. f(x)=x4-8x²+9
4. f(x)=x³+6x²+9x+3
Determining the proportional rates of growth for the following function: 0.015531t t Pe Derive a general expression for the proportional rate of growth. (1 mark) Calculate the proportional rates of growth at t = 5.
Convergence test for "\\displaystyle\\sum_{n=1}^\\infty \\frac{sin(n)}{n}".
The functions f and g are defined by f(x)=1/|1-3x| and g(x)=log1/3(1 /3x-2)-log3(x) respectively
1.1. Write down the sets Df(the domain of f) and Dg(the domain of g)
1.2. Solve the inequality f(x) greater than 2 for x"\\in" Df
1.3. Solve the inequality g(x) greater or equals to 0 for x"\\in" Dg
Hint: use the change of base formula
A space probe in the shape of the sphere x ^ 2 + y ^ 2 + z ^ 2 = 30 enters Earth's atmosphere and its surface begins to heat. After 1 hour, the temperature at the point (z. y. :) on the probe's surface is T(x, y, z) = x - 2y + 5z Find the hottest point on the probe's surface.
