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og sinx cost D Check if the integral Sinx cosx dx is aboulte convergent, conditionally convergent or divergent let f«) contiewos, positive, decreasing function (0,1] such that SEGAOX convergent. Prove: lim xfx=0 on Xtot 5 let f be integrable function on [1]. foss x H XE [o,(Excluding some points). Prove that $x + 6) dx = }} Tip is for integrable, so is xf(x)
4. Solve for x, 0 SX < 360° a) 2 sinx + 3 = 0 b) 7cosx + 2 = 0 c) 2sinx - sinx = 0 d) 2cos2x - cosx - 1 = 0
-olve the integration of COSX dx by combination of substitution and partial sin x + sinx raction methods.
0 bie 3x2_1 e CX 3x)2 dx 2 esco cos va va dx 3 l sinx sec? (cosx) dx • 7/2 cosx sin (sinx) dx 10 s S; X=(1+2x9) "dx x2 sixe dx @[Cittam bjpecede 8 4+3x sin (lax)
verify the identity tan(x+(5\pi )/(4))=(sinx+cosx)/(cosx-sinx)
Find the integral. write your answer in the simplest form. [CSC(sinx)cosx dx cos5x dx (1 +2sin5x)4 4.
Prove the identity. cscx - sinx = cotx cosx Note that each Statement must be based on a Rule chosen from the Rule menu. To see a detailed description of a Rule, select the More Information Button 1 the right of the Rule. Prove the identity. Note that each Statement must be based on a Rule chosen from the Rule menu. To see a detailed description of a Rule, select the More Information Buttor the right of the Rule.
4. Find the following limits by using L'Hôpital's rule. 1 + a) lim.-o 3 x cosx-sinx b) lim-o x sinx lim x-1x-1. c) 4. Find the following limits by using L'Hôpital's rule. 1 + a) lim.-o 3 x cosx-sinx b) lim-o x sinx lim x-1x-1. c)
If cosx and sinx are solutions of y'' + ay' + by=0, where a and b are constants, then a particular solution of y' + ay'+by = a +1+btanx is Select one: a. 1+sinx Insecx + tanx b.1-COSX In|secx +tang | C. 1- COSY d. 1 e. -COSX Inse Cx+tang | f. tanx Insecx + tanx| 2. COSX InseCX + tan| h. 1-sinx Insecx + tanx|
please solve and explain detailed sinx + cosx= 1 sin (x) + cos(x) = 1