# 0 a Gt1qt 191 Btap 01 Sv Function 01

Description
Description:
Categories
Published

View again

All materials on our website are shared by users. If you have any questions about copyright issues, please report us to resolve them. We are always happy to assist you.
Share
Transcript
Calculus 1 (MT 1004) 191 – Exercises 01 1/ Find the domain and the range of ( ) 2 4  x x x f   −=  2/ For pictures 7 – 10, determine whether the curve is the graph of a function of x. If it is, state the domain and range of function. 3/ a/ Find the equation of the line segment joinings the points (1, –3) and (5, 7). Is this equation nonlinear?  b/ Find the equation of the top half of the circle ( ) 42 22 =−+  y x  4/ Find expressions for the quadratic functions whose graph are shown: 5/ Find an expression for a cubic function f: ( ) 61  =  f  &  ( ) ( ) ( ) 0201  ===−  f  f  f   6/ Three runners compete in a 100 – meter race. The graph describes the distance run as a function of time for each runners. Describe in words what the graph tell you about this race. Who won the race? Did each runner finish the race? 7/ The manager of s furniture factory finds that it costs 2200k to manufacture 100 chairs in one day and 4800k to produce 200 chairs in one day. a/ Express the cost as a function of the number of chairs produced, assuming that it is linear. Then sketch the graph.  b/ What is the slope of the graph and what does it represent? c/ What is the y – intercept of the graph and what does it represent? 8/ Find the domain of each function: a/ ( ) 22 1 11  x x ee x f  − −−=  b/ ( )  t  t g 21 −=  9/ Sketch the graph: a/ ( )  t t t  f  6 2 −=  b/ ( ) 5 −=  x xg  c/ ( ) ⎪⎩⎪⎨⎧>−≤≤−− −<+= 3,633,2 3,9  x x x x x x f   Topic: Exponent (Stewart , Section 1.5).  10/ (Exercises 24) Suppose you are offered a job that lasts one month. Which of the following methods of payment do you prefer? a/ One million dollars at the end of the month.  b/ One cent on the first day of the month, two cents on the second day, four cents on the third day, and, in general, 1 2  − n  cents on the n th day, Topic: Inverse and logarithmic (Stewart , Section 1.6). 11/ A function is given by a table of values of a graph. Is it one – to – one? 12/ (Exercises 9 →  12) A function is given by a formula. Is it one – to – one? a/ f(x) =  x x 2 2 −   b/ ( )  x x f  310 −=  c/ g(x) =  x 1  d/ g(x) =  x cos  13/ (Exercises 21 →  16) Find a formula for the inverse of the function a/ ( )  x x f  310  −=   b/ ( ) 3214 +−=  x x x f   c/ ( )  x x ee x f  21 +=  d/ ( )  x x x x f  126 23 +−=  14/ (Exercises 61) Consider a bacteria population starts with 100 bacteria and doubles every three hours. Let n = f(t) be the number of bacteria after t hours. a/ Find f(t)  b/ Find the inverse of this function and explain its meaning. c/ When will the population reach 50000? 15/ (Exercises 62) When a camera flash goes off, yhe batteries immediately begin to recharge the flash’s capacitor, which stores electric charge given by ( ) ⎟⎟ ⎠ ⎞⎜⎜⎝ ⎛ −=  − at  eQt Q 1 0 . (The aximum charge capacity is Q 0  and t is measured in seconds). a/ Find the inverse of this fnction and explain its meaning.  b/ How long does it take to recharge the capacitor to 90% of capacity if a = 2. 16/ (Exercises 69) Prove that ( ) 21 1sincos  x x  −= −  16/ (Exercises 70 →  72) Simplify the expression a/ ( )  x 1 sintan  −  b/ ( )  x 1 tansin  −  c/ ( )  x 1 tan2cos  −  Topic 4: Hyperbolic functions (Stewart , Section 3.11) 17/ (Exercises 1 →  6) Find the numerical value of each expression a/ 0sinh b/ 0cosh c/ 0tanh d/ 1tanh e/ ( ) 2lnsinh f/ 3cosh g/ 1cosh 1 −  h/ 1sinh 1 −  18/ (Exercises 11) Prove the identity: ( )  y x y x y x sinhcoshcoshsinhsinh  +=+  19/ According to the next identity ( )  y y y x y x sinsincoscoscos  −=+ , let guess the similar identity for hyperbolic functions. Write it down and prove it. 20/ (Exercises 20) If 1312tanh  =  x , find the value of the other hyperbolic functions at x. 21/ (Exercises 21) If 35cosh  =  x  and 0 >  x , find the value of the other hyperbolic functions at x. 22/ Show that ( )  x x f  sinh =  is one – to – one. Find explicitly formula for 1 −  f  . ------------------------------------------------------------------------------------------------------------

Sep 22, 2019

#### 0_Hyundai All PDF

Sep 22, 2019
Search
Similar documents

View more...
Tags

## Equations

Related Search
Thank you for visiting our website and your interest in our free products and services. We are nonprofit website to share and download documents. To the running of this website, we need your help to support us.

Thanks to everyone for your continued support.

No, Thanks
SAVE OUR EARTH

We need your sign to support Project to invent "SMART AND CONTROLLABLE REFLECTIVE BALLOONS" to cover the Sun and Save Our Earth.

More details...

Sign Now!

We are very appreciated for your Prompt Action!

x