Assignment:
Hyperbolic functions
Q1. Find the numerical version of each expression
1) sinh 0
2) cosh 0
3) tanh 0
4) tanh1
5) sinh1
6) cosh1
7) sech 0
8) sinh(ln 2)
9) cosh(ln3)
10) cosh^-1 1
11) sinh^-1 1
Q2. Use definitions of hyperbolic functions to find each.
1) lim as x approached infinity tanh x
2) lim as x approached infinity sinh x
3) lim as x approached infinity sech x
4) lim as x approached infinity coth x
5) lim as x approached - infinity csch x
6) lim as x approached - infinity sinh x
7) lim as x approached - infinity tanh x
8) lim as x approached 0+ coth x
9) lim as x approached 0- coth x
Q3. Find the derivative
1) f(x)= tanh 4x
2) f(x)=xcoshx
3) h(x)=sinh(x^2)
4) g(x) = (1-cosh x) / (1+cosh x)
5) h(t) = coth(SQRT 1+t^2)
6) h(t)=tanh(e^t)
7) y=e^(cosh(3x))
8) y=tanh^-1 * (SQRT x)
9) f(t)=ln(sinh t)
10) f(x) = sinh x * (tanh x)
11) y=sinh(cosh x)
12) y=x tanh^-1 * (x) + ln(SQRT(1-x^2))
Provide complete and step by step solution for the question and show calculations and use formulas.