Question: Evaluate limc→0 1-cos 16ccsin 8c cos c


A ) 8
B ) 16
C ) 0
D ) ∞
E ) 1 / 8

Steps to derive

1 limc→0 1-cos 16ccsin8c cosc = limc→0 2sin28ccsin8c cosc

2 = 2limc→0 sin 8cccos c
 [Cancel the common factor.]

3 = 2(limc→0 sin8c / c)(limc→0 1 / cosc)
 [Use the product rule of limits.]

4 = 2(8)(1 / 1) = 16
 [Use limc→0 sin kcc= k and evaluate the limits.]

5 limc→0 1-cos 16ccsin 8c cos c = 16



Hence the right answer is Option B

Click Here To Go Back


Explore Related Questions

  • Evaluate: lima→0 [cos 2a-cos 6aa2]..
  • Evaluate: 19[lim6y→π 1-sin 3ycos 3y(π-6y)]..
  • Evaluate: limm→0 (cos 27m-cos 25mcos 25m-cos 23m)..
  • Evaluate: limz→0 (sin z sin 2z sin 3z......sin 28z..
  • Evaluate: limk→0 [sin 18k-sin 16ksin 22k-sin 20k]..
  • Evaluate: limv→0(sin 30v-sin 28vv)..
  • Evaluate: limq→π2 [sec 13q - tan 13q + 15]..
  • Evaluate: lims→0((40+s) sin (40+s)-40 sin 40s)..
  • Evaluate: limk→0(sin(35+k)-sin(35-k)k)..
  • Evaluate: limx→π2(2+2sin311xcos211x)..
  • Evaluate: limz→0 [1-cos 8z1-cos 12z]..
  • Evaluate: lima→0 [cosec 12a - cot 12aa]..
  • Evaluate: limx→0 sec 10x - 1x2(1 + sec 10x)2..
  • Evaluate: limc→0 [tan 20c - sin 20c100c3]..
  • Evaluate: limx→π16 [5-5sin 8x(π-16x)2]..
  • Evaluate: limx→01-cos (1-cos 6x)x4..
  • Evaluate: limu→21π2+ (7tan u+12)..
  • Evaluate: lima→0 [sina+sin2a+sin3a+...+sin 30asina+sin3a+sin5a+...+sin 9a]..
  • Write the equation of the horizontal asymptote of the curve y = 47x7+9x6...
  • Evaluate: limw→11π- (3cot w+5)..
  • Evaluate: limu→5+ln(9u-5)..
  • Find the equation of the horizontal asymptote of the curve y = 12x6+94x6+5x5+13...
  • Evaluate: limw→0+(ln(6sin 3w))..
  • Evaluate: limu→9π2+(4sec u+9)..
  • Write the equation of the horizontal asymptote of the curve y = 9sin 4x+1444x...
  • Write the equation of the horizontal asymptote of the curve y = 45cos 6x+549x...
  • ABCD is a square. The coordinates of C are (- 4, - 4). What are the coordiantes of A?..
  • PQRS is a rectangle. The coordinates of M are M(8, 0) and N are N(0, 4). What are the coor..
  • Find the equations of the horizontal asymptotes of the curve y = 10e9x+85e9x+13...
  • Write the equation of the horizontal asymptote of the curve y = 8x+84x-3...
  • Write the equation of the horizontal asymptote of the curve y = 5 arccsc 2x + 2...
  • Find the equation of the horizontal asymptote of the curve y = 3 e- 12x + 11...
  • Write the equation of the horizontal asymptote of the curve y = 28 arcsec 7x...
  • Write the equation of the horizontal asymptote of the curve y = 11 arccot 6x...
  • Write the equation of the horizontal asymptote of the curve y = 5 ln(3x+63x-3) + 8...
  • Find the equation of the horizontal asymptote of the curve y = 3e-x4 + 8...
  • OPQR is a Rhombus. Find the coordinates of Q and R, if the coordinates of P are P(3, 6)...
  • ABCD is a parallelogram. The coordinates of B and C are B(3, - 3) and C(4 , 3). Find the..
  • Find the equation of the horizontal asymptote of the curve y = 20x105x10+9x9+8..
  • PQRS ia a parallelogram. Coordinates of Q and R are Q(8, 2) and R(4, - 2). What would be t..
  • Evaluate: liml→0+ [46|l|9l]..
  • In the kite MNOP, diagonal OM divides diagonal NP in 1 : 3 ratio. The coordinates of N are..
  • Find the equation of the horizontal asymptote of the curve y = 42x8+8x7+8...
  • Evaluate: limt→0 [16t3|t|]..
  • Write the equation of the horizontal asymptotes of the curve y = 4 arctan11x..
  • OQ = 10. m∠ORQ = 90, PM = 3 RM. Write the coordinates of P...
  • Evaluate: limy→3+ [|y2-14y+33 |(y-3)]..
  • Evaluate: limt→2- [(t-2)|t2-12t+20|]..
  • Evaluate: limt→11-|t2-17t+66||t2-23t+132|..
  • The vertices of quadrilateral OABC are O(0, 0), A(28, 0), B(24, 8) and C(8, 24). Find the ..