Related InterviewSolutions

• The valuses of x for which `1+x log_e (x+sqrt(x^2+1)) le sqrt(x^2 +1)` areA. `x le 0 `B. `0 le x le 1`C. `x ge 0 `D. none of these
• `(1+x)^n le 1+ x^n` whereA. `n gt 1`B. `0 le n le 1 and x gt 0 `C. `n lt 1 and x lt 0`D. `x lt 0 `
• If the function `f(x)=cos|x|-2a x+b`increases along the entire number scale, then(a) `a=b`(b) `a=1/2b`(c) `alt=-1/2`(d) `a >-3/2`A. `a le b `B. `a=b/2`C. `a lt - 1/2`D. `a gt - 3/2`
• If `f(x)=unerset(x^2)overset(x^(2+1))e^(-t^2)` dt then f(x) increases onA. `(-2,2)`B. `(0,oo)`C. `(-oo,0)`D. none of these
• Find the value of `a`in order that `f(x)=sqrt(3)sinx-cosx-2a x+b`decreases for all real values of `xdot`A. `a lt 1`B. ` a le 1`C. ` a le sqrt(2)`D. `a lt sqrt(2)`
• The function` f(x)=tan^(-1)x-x` is decreasing on the setA. RB. `(0,oo)`C. R-[0]D. none of these
• For what value of a,`f(x)=-x^3+4ax^2+2x-5` decreasing for all x .A. (1,2)B. (3,4)C. RD. no value of a
• A function is matched below against an interval where it is supposed tobe increasing. Which of the following parts is incorrectly matched?Interval,Function[2, `oo)`, `2x^3-3x^2-12 x+6``(-oo,oo)`, `x^3=3x^2+3x+3``(-oo-4)`, `x^3+6x^2+6``(-oo,1/3)`, `3x^2-2x+1`A. `{:("","interval","Function"),((a),(-oo,-4],f(x)=x^3+6x^2+6):}`B. `{:("","interval","Function"),((a),(-oo,1//3],g(x)=3x^3-2x+1):}`C. `{:("","interval","Function"),((a),(2,oo],h(x)=2x^3-3x^2+12x+6):}`D. `{:("","interval","Function"),((a),(-oo,oo],q(x)=x^3-3x^2+3x+3):}`
• Let the function `f(x) = tan^(1-) (sin x + cos x)` be defined on `[ 0, 2 pi] Then f(x) isA. increasing on `[0,pi//4) cup [ 5 pi/4, 2 pi]`B. decreasing on `(Pi//4,2pi)`C. increasing on `(0,pi//4,) cup (3 pi//4,2pi)`D. decreasing on `[pi//4,7 pi//4]`
• the function `f(x)=logx/x` is increasing in the intervalA. `(1,2e)`B. `(0,e)`C. (2,2e)D. (1/e,2e)