Search & Filtering
Graph each function. Then identify the vertex, two points, domain, and range.
f(x) = |-1/5(x + 5)| + 2
square as a function of the length of its diagonal.
20. Suppose the average family spends 25% of its income I on food F, and 10% of this amount
F is spent on junk food J. Write J as a function of I.
21. Cliff left point A at 8 A.M. walking east at 3 kph. Renz left point A at 9 A.M. walking north
at 4 kph.
(a) Express the distance between Cliff and Renz as a function of the elapsed time
thereafter. Show that distance travelled is a function of time and find the rule of the
function.
12. A man jogs for 20 minutes at a rate of 6 kph, then walks for 30 minutes at a rate of 3 kph,
then sits and rests for 15 minutes and finally walks for 45 minutes. Find the rule of the
function that expresses his distance travelled as a function of time
6. The area of a rectangle is 100 m2. Express the perimeter as a function of the length of one
of its sides.
7. A right circular cone is inside a cube. The base of the cone is inscribed in one face of the
cube and its vertex is in the opposite face. Express the volume of the region between the
cone and the cube as a function of the length of the edge of the cube.
Consider the surface S = n (x, y, z) | z = p x 2 + y 2 and 1 ≤ z ≤ 3 o .(a) Sketch the surface S in R 3 . Also show its XY-projection on your sketch. (2) (b) Evaluate the area of S, using a surface integral
Question No#08
Find the limit of each rational function as 𝒙 → ±∞. 𝑓(𝑥) = 3𝑥 + 7
𝑥2 − 2
𝑓(𝑥)= 10𝑥5 +𝑥4 +31. 𝑥6
Question No#10
Let
ƒ(x) = 𝑥1/(1−x) .
Make tables of values of ƒ at values of x that approach x = 1 from above and below. Does ƒ(x)
appear to have a limit as x approaches 1? If so, what is it? If not, why not?
Question No#11
Find the limits using 𝐥𝐢𝐦 𝐬𝐢𝐧 𝜽 = 𝟏 𝒙→𝟎 𝜽
a) lim 6𝑥2(cot 𝑥)(csc 2𝑥) 𝑥→0
𝑏) lim sin 3𝑦 cot 5𝑦 𝑦→0 𝑦 cot4𝑦
Question No#13 Let h(𝑥) = 𝑥2−2𝑥−3
a) Make a table of the values of h(x) at x = 2.9, 2.99, 2.999, and so on. Then estimate limh(𝑥). What estimate do you arrive at if you evaluate h at x = 3.1, 3.01, 3.001 ...
𝑥→3
instead?
b) Support your conclusions in part (a) by graphing h near x = 3 and using that graph to
estimate h(x) on the graph as x approaching 3.
c) Find lim h(𝑥) algebraically.
𝑥→3
Let 𝑔(𝜃) = sin 𝜃 𝜃
a) Make a table of the values of g at values of u that approach 𝜃0 = 0 from above and below. Then estimatelim 𝑔(𝜃)
𝜃→0
b) Support your conclusion in part (a) by graphing g near 𝜃0 = 0
