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AllQuestion and Answers: Page 619
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Question and Answers Forum |
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AllQuestion and Answers: Page 619 |
| show that i^i is always real |
| prove that (1+cos θ+isin θ)^n + (1+cos θ−isin θ)^n =2^(n+1) cos (θ/2)cos ((nθ)/2) |
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| Compare: 2^2^2^.^.^. and 3^3^3^.^.^. Here it is raised 1001 times a square, 1000 times a cube. |
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| Compare: 2^2^2 and 3^3^3 |
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| ∫_0 ^( ∞) ((ln(⌊x^2 ⌋!))/( (x^x +1)^x )) dx |
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| Find two possible values of p if the lines px−y=0 and 3x+y+1=0 intersect at 45° |
| ∫_0 ^( ∞) ((ln x)/( (√x) (√(x+1)) (√(2x+1)))) dx |
| ∫_0 ^( ∞) ((x−1)/( (√(2^x −1)) ln(2^x −1))) dx |
| ∫ (log x + 1)x^x dx |
| ∀x,y∈R_+ ^∗ , show that (x/(x^4 +y^2 ))+(y/(y^4 +x^2 ))≤(1/(xy)) |
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| ((cos (((5π)/2)−6x)+sin (π+4x)+sin (3π−x))/(sin (((5π)/2)+6x)+cos (4x−2π)+cos (x+2π))) =? |
| ∫_0 ^( 1) ((tan(x^2 +1))/(x^2 +1)) dx |
| { ((a^2 =2a+b)),((b^2 =a+2b)) :} and a≠b find (√(a^2 +b^2 +1)) |
| ∫ln(sinx)=? x ≠ 0 + 2kπ ; k ∈ Z |
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| if x;y;z;t∈R and x+y+z ≤ 3t ; y+z+t ≤ 3x z+t+x ≤ 3y ; t+x+y ≤ 3z compare: x;y;z;t |
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| if x∈R prove that: x^6 - x + 1 > 0 |
| z^2 −7z+16=i(z−11) |
| ∫((xdx)/(x^4 +4x^2 +5)) |
| if f(x) = x^2 - 2x + 2 and g(x) = (√x) + 1 find [ f o g ] (x) = ? |
Pg 614 Pg 615 Pg 616 Pg 617 Pg 618 Pg 619 Pg 620 Pg 621 Pg 622 Pg 623 |