Tìm nghiệm của phương trình $\sin^2x = \frac{1}{2}$ dưới dạng $a + bi$.

A curve has slope 2x + 3 at each point (x, y) on the curve. Which of the following is an equation for this curve if it passes through the point (1, 2) ? Trigonometric identities are equations that hold true for all values of the variable where both sides of the equation are defined. x2 sin(2x)dx using a suitable integration technique. Ans We should use ... −(1/2+2/3). 1 −. 2 u. −2/3. = u. −7/6. 1 + O(u. −1. ) where the big-O ... sin 2x. Examples. 1. To compute / sin4x dx we have to use two identities: sin2x ... 1 - 2 cos 2x + cos2 2x dx. = 1. 4 x -. 1. 4 sin 2x +. 1. 4. ∫ cos2 2x dx. First, we use the trig identities: cos2x=cos^2x-sin^2x, cos^2x+sin^2x=1 and sin2x=2sinxcosx to transform the integral to ∫(cos2x)/(1+sin2x)dx. ... x) 2·5-(-1) (2). (g(x)). 22. 10-2. 8. 4. =2. 4. 16. If y. 5x√x²+1, then dy at x. 3 is ... The function ƒ is defined by f(x) = sin x + cos x for 0 ≤ x ≤ 2л. 2e2x - sinx. 1. = 2e0 - sin 1 = 2. Since lim x→0. (e2x - cosx) = e0 - cos 0 ... (a) limx→0(1 + 2x)1/x. Solution. Since (1 + 2x)1/x = e. 1 x loge(1+2x) ... ... 1)2 = n2 − n − 1 = n(n − 1) − 1 . Therefore n. X k=1 bx2 kc = bx2 ... sin 2x. , whence sin 2x = 1. 2 . Therefore x = (−1)k π. 12. + kπ. 2. , where k is ... (sin x) ln(1 − 2x), up to x4. Solution: Find the expansions for the two ... 1 − 1/2 (2x) + 3/22 (2x)2/2 − 15/23 (2x)3/6 + ... true for −1 < 2x < 1. x sin( (1 - x)t) - (1 - x) sin(xt) = tx( 1 - x)(2x - 1) t3 + x( 1 - x) t5p3 and x(1-x) t2. XCOS((l-x)t)+(l-x)COS(Xt)=1-. 2. +x(1 -x) t4p,, where l~~l<&and lp41 ...