Higher Engineering Mathematics, Sixth Edition
182 Higher Engineering Mathematics (b) 0 2 2 1 3 3 2 ycos 2 ycos yx yx 3 6 4 2 0 2 4 (a) (^6) x y (c) 1120 2 ...
Functions and their curves 183 For example, if f(x)=(x− 1 )^2 ,anda= 1 2 ,then f(ax)= (x 2 − 1 ) 2 . Both of these curves are sh ...
184 Higher Engineering Mathematics and graphs ofy=lnx and y=−lnx are shown in Fig. 18.19(b). Problem 1. Sketch the following gra ...
Functions and their curves 185 4 10 20 y(x2)^3 (c) –10 –20 (^202) x y 4 10 20 y 5 (x2)^3 (d) –10 –20 (^202) x y Fi ...
186 Higher Engineering Mathematics Now try the following exercise Exercise 77 Further problems on simple transformations with cu ...
Functions and their curves 187 Odd functions A functiony=f(x)is said to beodd iff(−x)=−f(x) for all values of x. Graphs of odd f ...
188 Higher Engineering Mathematics (a) A graph ofy=lnx is shown in Fig. 18.29(a) and the curve is neither symmetrical about the ...
Functions and their curves 189 y y 52 x 11 4 y^5 x 2 234 1 21 0 1 21 x y5 2x 2 12 Figure 18.30 y y 5 x y 5 x y 5 x^2 4 (^123) x ...
190 Higher Engineering Mathematics (c)arccos ( − √ 3 2 ) ≡cos−^1 ( − √ 3 2 ) = 150 ◦ = 5 π 6 rador2.6180rad (d)arccosec( √ 2 )=a ...
Functions and their curves 191 A y B C D 2 3 4 5 24 23 22 0 1 2 3 4 21 22 23 24 25 21 x 12 y (^5) x 11 x 12 y (^5) x 11 1 x Figu ...
192 Higher Engineering Mathematics 28 26 26 24 24 22 21 0 1 4 6 2 2 (^468) x y y 5 x^23 2 x 11 y 52 xx^2131 x (^5212) y (^512) F ...
Functions and their curves 193 Problem 9. Determine the asymptotes parallel to thex-andy-axes for the function x^2 y^2 = 9 (x^2 ...
194 Higher Engineering Mathematics x 521 y^5 x^2 2 y(x 1 1) 5 (x 2 3)(x 1 2) y(x 1 1) 5 (x 2 3)(x 1 2) 210 28 26 24 22 26 24 22 ...
Functions and their curves 195 Hence y=mx+c=± 1 x+0, i.e.y=x and y=−x are asymptotes. To determine any asymptotes parallel to th ...
196 Higher Engineering Mathematics 22 24 22 24 26 2 2 4 6 (^04) x y y 5 x (^211) x y 5 x (^211) x y^5 x Figure 18.35 18.8 Brief ...
Functions and their curves 197 18.9 Worked problems on curve sketching Problem 13. Sketch the graphs of (a)y= 2 x^2 + 12 x+ 20 ( ...
198 Higher Engineering Mathematics x 3 y 1 14 24 x y x y (a) x 5! (9 2 y^2 ) (b) y^2516 x (c) xy 55 Figure 18.37 Problem 15. Ske ...
Functions and their curves 199 x^2 +y^2 = 4 .Comparing this equation with x^2 +y^2 =a^2 shows thatx^2 +y^2 =4 is the equa- tion ...
200 Higher Engineering Mathematics x=^13 √ ( 36 − 18 y^2 ) ⎡ ⎢ ⎢ ⎣ ellipse,centre( 0 , 0 ), major axis 4 units alongx-axis, mi ...
Functions and their curves 201 24 8 10 15 9. 10. 5 (^0) x y 6 y 5 (x 2 4)^2121 0.50 0.25 (^0) x y y 5 x 2 x^2 y 5 ...
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