3. (a) (2 marks) Evaluate the limit lim x0 1 - cos(x) x Hint: Multiply both...

Transcribed Image Text:

3. (a) (2 marks) Evaluate the limit lim x0 1 - cos(x) x Hint: Multiply both numerator and denominator by 1 + cos(x), then use the result known from class: lim sin(x) x0 = 1. (b) (2 marks) The function f(x) is defined as x+2a cos(x) x 0 f(x)= = 1 cos(x) x > 0 x where a is some unspecified constant. Use your result in part (a) to determine the value of the constant a so that f(x) is continuous at x = 0. 3. (a) (2 marks) Evaluate the limit lim x0 1 - cos(x) x Hint: Multiply both numerator and denominator by 1 + cos(x), then use the result known from class: lim sin(x) x0 = 1. (b) (2 marks) The function f(x) is defined as x+2a cos(x) x 0 f(x)= = 1 cos(x) x > 0 x where a is some unspecified constant. Use your result in part (a) to determine the value of the constant a so that f(x) is continuous at x = 0.

Answer rating: 100% (QA)

Soln3 a We have to calculate the limit lim 1Cass 5170 lim 5170 lim Lossy 1ush 2 bato ... View the full answer