calculus soruları

Chapter 1 : EQUALITY, LOGARİTHM and FUNCTION

Lineer Inequalities

Solve that inequality

Quadratic Inequalities

x2 – x – 6 > 0 Solve that inequality

Solve for x if sin2x – 3cos2x + 2 = 0 is given where xÎ [ 0,2p]

Suppose you are given points A(-2,3) and B(3,5) , write the equation of the line.

Find the intersection of 2x + 3y = 6 and x – 2y = -2

Given x2 + y2 + 6x – 2y + 6 = 0 is the eq. of the circle. Find center, find radi.

Sketch y = x ¹ -2

Sketch y = | x |

Sketch y = 2| x | + 3

Sketch y = | x - 2|

Sketch y = | x + 1| - 3

Describe the graph of the given equation x2 + y2 + x = 0

Find an equation of the perpendicular bisector of the line segment joining points. (2,1) and (1,2)

Sketch the graph of y = | x + 1 | + | x – 1 |

Ex: Find the domain of f(x) =

Ex: Find the domain of f(x) =

Ex: Find the domain of f(x) =

Ex: Find the domain of f(x) =

Ex: Consider g(x) = Try to write it is a composition of two functions

1. f(x) = ; h(x) = | x | Þ g(x) = f o h =

2. f(x) = ; h(x) = 1 + | x | Þ g(x) = f o h =

3. f(x) = ; h(x) = x² Þ g(x) = f o h =

Ex: f(x) = g(x) = - x2 compute domain of fog and gof

Ex: Find the domain and range of y = 2 +

Ex: Using the logarithmic properties rewrite the expressions below in terms of lna, lnb , lnc a) ln a2 b) ln c) ln d) ln

a) ln a² =

b) ln =

c) ln =

d) ln =

Ex: Rewrite the expressions below as a single logarithm a) 4 log 2 – log 3 + log 16 b) log x – 3.log 2x + 3.log 2 c) 2.ln (x+1) + ln x – 2.ln

a) 4 log 2 – log 3 + log 16 =

b) log x – 3.log 2x + 3.log 2 =

c) 2.ln (x+1) + ln x – 2.ln =

Ex: Find the domain of the following function f(x) = log3

Ex: Consider f(x) = , sketch the graph, find the domain and range

Ex: Consider f(x) = , sketch the graph, find the domain and range

Ex: Find the domain and range, and draw the graph of; f(x) =

Ex: Find the domain and range of f(x) = | x | then draw it’s graph

Ex: f(x) = , find domain , range and draw it’s graph

Ex: f(x) = Find the domain, range and draw graph

Ex: Given f(x) = x2 + 3x – 4 Find a) f(x+h) b) f(x) + f(h)

Ex: Given f(x) = , g(x) = find the domain of; a) (f+g)(x) b) (f-g)(x) c) (f.g)(x) d) ()(x)

a) (f+g)(x) = f(x) + g(x) =

b) (f-g)(x) = f(x) -g(x) =

c) (f.g)(x) = f(x) . g(x) =

d) ()(x) =

Ex: f(x) = 2x + 7 g(x) = x2 – 8 a) (fog)(x) b) (fof)(x)

a) (fog)(x) = f( g(x) ) =

b) (fof)(x) = f( f(x) ) =

Ex: Find the domain of (fog)(x) if f(x) = , g(x) 2x - 3

Ex: Consider the following functions; f(x) = g(x) = x + 1 h(x) =

Chapter 2 : LIMIT

Ex: Find the limits of the following functions. a) (x3 + 4x2 – 3 ) b) c)

a) (x³ + 4x² – 3 ) =

b) =

c) =