Question

give answer of all the questions plzzźzzzzz and full explanation

Answer 1

this is obtion based question check all options

a) f(x) = ln{x+√(1+x^2)}

put x = -x

f(-x) = ln(-x+√(1+x^2))

add f(x) and f(-x)


f(x) + f(-x) = ln(x^2+1-x^2) =0

hence f(x) is an odd function so, option (a ) is wrong .


2) d{(sin(t^2).dt}/dx = -sinx^2


differentiate wrtx x below function


d{sin(t^2)dt}/dx = -sinx^2


hence, (b) is correct



3). option (c ) is also correct . because when we see graph of cosx ,. area in above part equal to area of below part . because both area are in opposite sign hence , area of this function inclosed by x -axis is equal to zero .


4) any function f(x) +g(x) is continuous only when f(x) and g(x) both are continuous .

example :-

f(x) = x^2 +1

g(x) = x+2

two continuous functions then ,

f(x) +g(x) = x^2 + x +3

this is also continuous so, option (d) is also correct .


5) x - y +2 =0 is a tangent of give function ,
at ( -1 , 1)

(x + y)^3 = (x -y +2)^2
slope of tangent

3(x + y)^2 (1 + dy/dx ) = 2(x - y +2 )(1 -dy/dx )

put x = -1 and y = 1

3(-1 +1)^2(1 +dy/dx) =2(-1-1+2)(1-dy/dx)

0 = 4(1-dy/dx)


dy/dx = 1

now equation of tangent ,

(y -1) - (x +1 ) =0

y - x -2 =0

e.g. x -y +2 =0. is tangent of given curve at (-1,1)
so, option (e). is correct