TRUE OR FALSE 6 i)cos(3pi/4)=1/root2 ii)Every function is either an even or odd

Question

TRUE OR FALSE 6 i)cos(3pi/4)=1/root2 ii)Every function is either an even or odd function? iii)The function cos(x) is invertible on [-pi/2,pi/2]? iv)The function e^x is the inverse of the function ln(x)? v)A sequence {a n} can have more than one limit? vi) The sequence {1,-1,1,-1} hastwo limits? vii) f(x)=x^2-1/x-1 and g(x)=x+1 are the same functions? viii)If lim(x-->a+) f(x) and lim (x-->a-) f(x) exists,then so does lim(x-->a) f(x)? xi)lim(x-->infinity) ln(x)/x^p=0? x)lim(x-->0) sin(theta)/theta XI)If lim(n->infinity) {an}=L and lim(n->infinity) {bn}=M, then lim(n->infinity) (an/bn)=L/M

Explanation / Answer

Please rate this..I've put lot of effort
1. cos(3pi/4)=cos(pi-pi/4)=-cos(pi/4)=-1/root2
hence false

2. every function can be written as sum of two even or odd function but not necessarily should be one.
hence false

3. cos function is invertible in the interval [0, pi]
hence false

4. In ln (x) , x can't take negative values but in e^x , x can take negative values.therefore e^x is not inverse function of ln(x)
hence false

7. both are not same because denominator x-1 becomes zero at x=1 , hence first function doesn't exist at x=1 but the later one does.
hence false

8. Not necessary .function may have discontinuity at that point.
hence false

9.applying L'Hospital rule and differentiating once we get the form of 1/x^q, where q>1...hence at x tends to infintiy limit is zero
hence true

10. limit sin(theta)/theta =1 as theta tends to zero by applying L'hospital rule

11. we can break limits to numerator and denominator separately
hence true.

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.