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Prime minister drinks the hotter coffee. The PM doesn’t gives time for heat transfer to happen, hence temperature is still the same, while for President has decreased.
[tanx= x + 1/3x^3 + 2/(15)x^5 + (17)/(315)x^7 + (62)/(2835)x^9 +...]
tanx= x + 1/3x^3+ 2/(15)x^5 + (17)/(315)x^7 + (62)/(2835)x^9+...] I hope u needed this only.
substitue y' =uy''=u'we get u'=2x/(x*x+1)uln(u)=ln(x^2+1)+C=> u=c(x^2+1)dy/dx=c(x^2+1)y=c((x^3)/3+x)+c1
dy/dx= cosx + sinx In first quadrant both are positive so increasing In second quadrant sinx is positive but cos x is negative till 135 magnitude of sinx > cosx so it will be positive Increasing...
Hi, Tangent to first parabola is y=mx+1/m If this is also the tangent to second parabola than put this equation in second parabola. Form a quadratic in x and put its d=0 as tangent and curve has only...
d/dx[ax+b] = d/dx[ax]+d/dx[b] =ad/dx[x]+0 a(1) =a
(y 2 +x 2 +2xy+y+x)/(y 2 +x 2 +2xy+2y+2x)= ((y+x) 2 +(y+x))/((y+x) 2 +2(y+x)) = (x+y+1)/(x+y+2) we can now solve the diff. eqn by substituting x+y=t
the result is very simple for circle centred at origin we say eqn of tangents is y=mx +/- r(1+m 2 ) 1/2 for circle with centre a,b we can linearly transform the eqn. by Replacing y------> y-b...
divide the whole equation with 5^x and you will get ans 1
For 1) ans is 1 2) ans is 32/3
limit is zero.
Answer: 4 Let (h,0) be the circle's center. h=1+r Equation of circle is: (x-h) 2 +y 2 =r 2 (x-1-r) 2 +y 2 =r 2 x 2 +y 2 -2x-2xr+2r+1=0 But y 2 =4x, Substituting we get: x 2 +2x-2xr+2r+1=0 x 2...