https://socratic.org/questions/how-do-you-differentiate-g-x-1-sin-2-2-x-1-cos-2-x-using-the-product-rule dxdg=−sin(4−2x)(1+cos2x)+sin2x(1+sin2(2−x)) ... How do you simpli...
lim(x->pi/2)(cos^2x)/(1-sin x) L'Hopital Rule: lim(x rightarrow b) (f(x))/(g(x))=lim(x rightarrow b) (f'(x))/(g'(x)) Applying it: lim(x->pi/2)(cos^2x)/(1-sin x)=lim(x->pi/2)(-2cosxsinx)/(-cosx) lim(x->pi/2) (2sinx) =2sin (pi/2)=2*1=1
Question: Find ∫sin5(2x)cos2(2x)dx. Integration by Substitution: We use the method of substitution to undo a chain rule. The basic formula is: If u=g(x) then ∫f(g(x))g′(x)dx=∫f(u)du. We often need to combine this with a bit of algebra or a trig identity to...
=sin2x+根号3(1+cos2x)+3-根号3 =sin2x+根号3cos2x+3 =2sin(2x+Pai/3)+3 故最小正周期T=2π/2=π f(A)=f(B)=2sin(2A+Pai/3)+3=3+根号3 即sin(2A+Pai/3)=根号3/2 因为三角形ABC中有，A=B，则有0<A<90,0<B<90 所以有Pai/3<2A+Pai/3<4Pai/3 所以有：2A+Pai...