cosh(0) = e^0 + e^-0 /2 = 1+1/2 = 2/2 = 1
sinh(pi) = e^iPi - e^-ipi / 2 = 0 - 0 /2 = 0/2 = 0
1. Ssinhx – cosh xd sinh x - cosh x 2 coth'(x) + 1 coth2(X) - 1 dx 3. S cosh² x dx 4. S sinhᵒ x dx ctanhx- sinh x sinh 2x
Recall three facts about hyperbolic cosine and hyperbolic sine functions: dr cosh(x) = sinh(x), di sinh(x) = cosh(x), cosh? (x) – sinh? (x) = 1. Compute the Wronskian of cosh(2) and sinh(2). Using your question 1's answer, cosh() and sinh(x) are linearly independent on R True False
Find the derivative of the following: f(x)=( Sinh(Sin-(x2)))3 оа. Select one: - 6X(Sinh(Sin-(x^))) Cosh(Sin-1(xº) √1-8" 3(Sinh(Sin-'(x2)))?Cosh(Sin-'(x2)) O b. 71-X 3(Sinh(Sin '(x2))) Cosh(Sin ?(X)) O c. 71-X 6XCosh(Sin-'(x?)) O d. V1-14
question 10 and 11 10. Solve the equation 5 cosh x – 3 sinh x = 5. 11. (a) Show that cosh (x - y) = cosh x cosh y - sinh x sinh y. (b) Show that for any real number x, cosh” x + sinh? x = cosh2x . Hence prove that cosh2x = 2 sinhạ x + 1 = 2 cosh? x - 1. 1+ tanh x (c) Show that 1- tanh x
2 -e Recall that cosh(x) er te 2 and sinh(2) Any general solution of y'' – y=0, can be written as y(x) = ci cosh(x) + C2 sinh(x), for arbitrary constants C1, C2. O True O False
abité -br and 2 Find the Laplace transform of sinh bt. Recall that cosh bt ebt -bi sinh bt = 2 -e ${sinh bt} b b2 - 52 S ${sinh bt} = $2 + b2 S ${sinh bt} = b2 - 52 b 52 - 62 ${sinh bt} S ${sinh bt} 32 - 62
Give an exact number thank you Evaluate the definite integral. 3 s cosh 22x sinh 2x dx 0
please reply me asap, tq 9. Evaluate cosh(y) +(c sinh(y)+e' cosh(y))dy + esinh(y)) ? Why is it path independent? (2%)
The hyperbolic cosine and hyperbolic sine functions, f(x) cosh(x) and g(x) sinh(), are analogs of the trigonometric functions cos(x) and sin(z) and come up in many places in mathematics and its applications. (The hyperbolic cosine, for example, describes the curve of a hanging cable, called a catenary.) They are defined by the conditions cosh(0)-l, sinh(O), (cosh())inh("), d(sinh()- csh) (a) Using only this information, find the Taylor polynomial approximation for cosh(x) at0 of COS degree n = 4. (b) Using only...
' ' 3. The hyperbolic trigonometric functions are defined by sinh(t) , The following identities might be helpful in the following problem. You should convince yourself that they are true, but you are not required to write up proofs/derivations cosh2 1-sinh2に1, cosh2 1 + sinh2にcosh(21), cosh 1 -sinh 1-cosh 1 sinh 1, dl dl (a) For a real number t, define sinh-1に1n(t + Vt2 + 1) Show that sinh(t) is the unique eaber u such that sinhu t (b) Use...