Question

Answer t or f. and justify.

a) there is a closest positive number to zero.

b) the function g(x)= e^cos x is periodic.

c) a/b + c/d= a+c/b+d

d) if y=7x+4 is a linear function then increasing x by 2 units increases the slope by 2 units.

Answer 1

a) supoose 0.1 is closest positive number . we know there is infinite number between two number(btween 0 and 0.1) so we can not say there is a closest number to zero so statement is false .

b)g(x)= e^cosx

we know cos (x+2pie) cosx

g(x+2pie)=e ^(cos(x+2pie))= e^cosx

g(x)=g(x+2pie) so g(x ) is periodic with period = 2pie

statement is true

c) a/b+c/d= ad+bc/bd so statement is false.

d) y = 7x+4 so slope = 7

x incresased by 2 now x = x+2

y = 7(x+2) +4 = 7x +16 here slope = 7 so slope doesnot change .statement is false