# Answer to Question #46101 in Algebra for Sapna

Question #46101

Which of the following statements are true? Give reasons for you answer. (This means that if you

think a statement is false, give a short proof or an example that shows it is false. If it is true, give a

short proof for saying so. For instance, to show that {1, Padma, blue} is a set’ is true, you need to

say that this is true because it is well defined collection of 3 objectives.)

(i) The domain of the function f given by

}. {1 \ R is

1 x

2 x

f(x)

2

2

(ii) Any curve with portions in the first and second quadrants is symmetric about y-axis.

(iii)

1

2

1

lim

1

lim

x x x

does not exist.

(iv) An ever function cannot be monotonic.

(v) The curve

) 1 (

1

) 4 (

2

2

x

y

has no asymptote parallel to axes.

(vi) A function f, defined by f(x) = x sin x + cos x, is decreasing in

. π/2 o,

(vii) If

1

1

, ) ( o dx x f

then f must be an even function.

(viii)

. cos cos sin

2 2

x x dt t

dx

d

x

x

(ix)

1 x 2 f(x) by given : f R R

is differentiable on R.

(x) The

think a statement is false, give a short proof or an example that shows it is false. If it is true, give a

short proof for saying so. For instance, to show that {1, Padma, blue} is a set’ is true, you need to

say that this is true because it is well defined collection of 3 objectives.)

(i) The domain of the function f given by

}. {1 \ R is

1 x

2 x

f(x)

2

2

(ii) Any curve with portions in the first and second quadrants is symmetric about y-axis.

(iii)

1

2

1

lim

1

lim

x x x

does not exist.

(iv) An ever function cannot be monotonic.

(v) The curve

) 1 (

1

) 4 (

2

2

x

y

has no asymptote parallel to axes.

(vi) A function f, defined by f(x) = x sin x + cos x, is decreasing in

. π/2 o,

(vii) If

1

1

, ) ( o dx x f

then f must be an even function.

(viii)

. cos cos sin

2 2

x x dt t

dx

d

x

x

(ix)

1 x 2 f(x) by given : f R R

is differentiable on R.

(x) The

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