Problems in Mathematical Analysis.pdf - pwp.net.ipl.pt

Sec. 2] Graphs of Elementary functions 19
tions:
Construct the graphs of the exponential and logarithmic func-
101. / = a x , if a = 2, l f
102*. y = \oga x, if a =10, 2, 1, *.
(?(e = 2, 718 ...)*).
103*. y = sinhx, where sinhx=l/2(e x
104*. f/ = coshx, where coshx =
105*. f/ = tanhx, where
106. 0=10*.
107*. y=-e~* 2
(probability curve).
108. ^ = 2"" *3
. 113. y =
109. //-logx 2
e -x ).
110.
.
y-=log
114. (/=--
2
111.
A:.
//=-log(logx).
115. = {/
116. = t/ log"(cosx).
112. /y==rV-- 117 - ^ = 2-^ sin*.
log X
Construct the graphs of the inverse trigonometric functions?
118*. y--=arc sin*. 122. # = arcsin~.
x
119*. j/ = arccosx. 123. # = arc cos--.
120*. # = arc tan*. 124. ^ = A: + arc cot x.
121*, (/= arc cot x.
Construct the graphs of the functions:
125. y=\x\.
126. y = ^(x + \x\).
127. a) y = x\x\\ b) y = log^^l x \-
128. a) t/= sinA:+ sin | jt|; b) f/= sin x |
129. ^-< _l. whcn
3 x 2 when |jc|< 1.
*) About the number * see p. 22 for more details.
sinx|.