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1. By using the formula, f^' (x)= lim┬(z→x)〖(f(z)-f(x))/(z-x)〗, find the derivatives of the following functions.
a) f(x)= 1/(x+2)
b) f(x)= 1/((x+2)²)
c) g(x)= x/(x-1)
d) g(x)=1+√x
a) f(x)= 1/(x+2)
b) f(x)= 1/((x+2)²)
c) g(x)= x/(x-1)
d) g(x)=1+√x
A jogger runs from her home to a point A, which is 6 km away. For there 6 km, she
begins by running at a constant speed till she reaches a hilly portion 2 km from her
home. Here her speed slows down while she runs up the hill, which is a 1-km run.
Then she speeds up while running down the hill. The last 2 km of the run are again at
constant speed. Draw a graph to show the jogger’s speed as a function of the distance
from her home. Also find the range of this function.
begins by running at a constant speed till she reaches a hilly portion 2 km from her
home. Here her speed slows down while she runs up the hill, which is a 1-km run.
Then she speeds up while running down the hill. The last 2 km of the run are again at
constant speed. Draw a graph to show the jogger’s speed as a function of the distance
from her home. Also find the range of this function.
Describe two situations that can be modelled with a Tree. Describe the graph model that you will use.
Describe two situations that can be modelled with a Graph. Describe the graph model that you will use
there are 25 applications for four software tester positions
what is the maximum number of relative extrema contained in the graph of this function?
f(x)=3x^3-x^2+4x-2
f(x)=3x^3-x^2+4x-2
one less than the product of four and a number
Log base 2 (x + 1) = 16 log base (x +1) 2
Bristowe has asked for your advice in evaluating the current phone reservation system. Create a simulation model to investigate her concerns. Make recommendations about the reservation agents.
Using computer technology (www.desmos.com or other mathematics graphing website) attach a graph of the parabola at midnight on the x-y axis keeping Des Moines at the origin and label the location of Columbus, Memphis, and Louisville on the graph. (Points may be added by hand to the computer generated graph).
Columbus, Ohio is 550 miles east and 80 miles south of Des Moines;
Memphis, Tennessee is 190 miles east and 430 miles south of Des Moines; and
Louisville, Kentucky is 420 miles east and 230 miles south of Des Moines.
a) For each of the above cities, state whether, by midnight, the city has already been affected by the front, is just about to be affected by the front, or has not yet been affected by the front.
b) How are your conclusions supported by the graph you drew in Step 5.
c) Support your conclusions using algebraic methods
Columbus, Ohio is 550 miles east and 80 miles south of Des Moines;
Memphis, Tennessee is 190 miles east and 430 miles south of Des Moines; and
Louisville, Kentucky is 420 miles east and 230 miles south of Des Moines.
a) For each of the above cities, state whether, by midnight, the city has already been affected by the front, is just about to be affected by the front, or has not yet been affected by the front.
b) How are your conclusions supported by the graph you drew in Step 5.
c) Support your conclusions using algebraic methods
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#332078 on Oct 2022
#332078 on Oct 2022