(a) Find the limit of the following functions:
-lim as x approaches 0 (1-cos3(x)/x)
-lim as x approaches 0 (sin(x)/2x)
-lim as theta approaches 0 (tan (5theta)/theta)
(b) Find the derivative of the following functions:
-f(x) = cos (3x2-2x)
-f(x) = cos3 (x2/1-x)
(c) Determine the period of the following functions:
-f(x) = 3 cos(x/2)
-f(x)= 21+ 7 sin(2x+3)
a) Evaluate the limit lim x→0 tan(2x) / x
b) Differentiate y = x^tan(x)
c) Find the equation of the tangent line to 4x^2 + 2xy−y^2 = 4
at the point (1, 2).
d) Differentiate f(x) = arctan(x^2 + 1)
e) Differentiate f(x) = ln(cosh x)
Thank you!
Use
the definition f '(x) = lim tends to 0 (f(x+h) - f(x) / h) to find
a. The derivative of f(x) = x + (30/x)
b. The derivative of f(x) = 3x^2- 5x + 30