Question

Tolong bantuannya gan, prioritas nomor 2 aja. Kalau dapat jawaban nomor yang lain gak apa juga.

Answer 1

1. lim(x→4) tan (x-√x -2)/(x-4)
    = lim(x→4) tan (√x+1)(√x-2)/(√x-2)(√x+2)
    = (tan (√x+1))/(√x+2) . (tan (√x-2))/(√x-2)
    = (√x+1)/(√x+2) . 1
    = (√4+1)/(√4+2)
    = 3/4

2. f(x) = 2x³ - 4x² + 16
    f'(c) = lim(h→0) (f(c+h)-f(c))/h   
           = lim(h→0) ((2(c+h)³ - 4(c+h)² + 16) - (2c³ - 4c² + 16))/h
           = lim(h→0) (2h(3c²+3ch-4c+h²-2h))/h
           = lim(h→0) 2.(3c²+3ch-4c+h²-2h)   ; c = 5
           = 2.(3c²+3c(0)-4c+(0)²-2(0))
           = 6c² - 8c

    f'(5) = 6(5²) - 8(5)
           = 150 - 40
           = 110

4. f(x) = (1+cos x)/(xsin x)
    f(x) = (sin² (x/2)+cos² (x/2)+cos² (x/2)-sin² (x/2))/(x.(2.sin (x/2)cos (x/2))
    f(x) = (2.cos² (x/2))/(x.(2.sin (x/2)cos (x/2))
    f(x) = cos (x/2))/(x.sin (x/2)
    
f'(x) =((xsin(x/2))(-(1/2)sin(x/2))-((1/2)xcos(x/2)+sin(x/2))co (x/2))/(xsin (x/2))²
f'(x) = (-(1/2)x.sin² (x/2)-(1/2)x.cos² (x/2)-sin (x/2).cos (x/2))/(x.sin (x/2))²
f'(x) = (-(1/2)x - (1/2)sin x)/(x.sin (x/2))²
f'(x) = -(x+sin x)/(2x².sin² (x/2)
f'(x) = -((x+sin x).cosec² (x/2))/2x²