Prove that sinhx =( e^x - e^-x/ 2), coshx = (ex+e^-x/2) is equal to: sinh x=...
Prove that
sinhx =( e^x - e^-x/ 2), coshx = (ex+e^-x/2)
is equal to: sinh x= x+x^3/3! + x^5/5! ... and cosh x= 1+ x^2/2! +x^4/4! ..
USE THIS EQUATION: e^x = sum x^n/ n! = 1+x+(x^2/2!) +(x^3/3! )
Homework Answers
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Prove that
sinhx =( e^x - e^-x/ 2), coshx = (ex+e^-x/2)
is equal to: sinh x=...
question 10 and 11 10. Solve the equation 5 cosh x – 3 sinh x =...
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
hat would be the partition function of this system according to equa tion 7.16? (e) W...
hat would be the partition function of this system according to equa tion 7.16? (e) W (f) What is the probability of finding both particles in the same single-par state, for the three cases of distinguishable particles, identical bosons, ane identical fermions? 4) The entropy of a two-state para magnet is given by S = Nk [ln(2 cosh x )-x tanhx ]], where x 2 uB kT Find the value of S at T-0 and T-oo. sinhx = "(ex-c"); coshx-(ex...
I need help with these problems please. Problem 1. Check (e^a)(e^b) = (e^(a+b)) by expanding both...
I need help with these problems please. Problem 1. Check (e^a)(e^b) = (e^(a+b)) by expanding both sides in double series in a and b up to fourth order as follows. Make a substitution a → at and b → bt and expand both sides in t up to (including) t4. Problem 2. Calculate the following sum, if convergent. Problem 3. By definition, cosh(x) = (ex + e−x)/2 and sinh(x) = (ex − e−x)/2. Find series expansion for cosh(x) and sinh(x)...
1. Ssinhx – cosh xd sinh x - cosh x 2 coth'(x) + 1 coth2(X) -...
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
2 -e Recall that cosh(x) er te 2 and sinh(2) Any general solution of y'' –...
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
Recall three facts about hyperbolic cosine and hyperbolic sine functions: dr cosh(x) = sinh(x), di sinh(x)...
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
5. (14,5) Here are some details about the function f(x) = cosh x. Use these details...
5. (14,5) Here are some details about the function f(x) = cosh x. Use these details and the formula for Maclaurin series to find the Maclaurin series for f(x) = cosh x. Write out at least 6 terms of your answer and give your answer in summation notation f(x) = coshx f'(x) = sinh x f"(x)=cosh x f(0) = cosh 0 = 1 f'(0) = sinh 0 = 0 6. (12,4) In polar coordinates the graph of r = 7+7sin()...
Please do both of them. Thank you. Find 3 cosh(2 x) 3 sinh(5 x)] 3 5...
Please do both of them. Thank you.
Find 3 cosh(2 x) 3 sinh(5 x)] 3 5 2+4 15 a) 225 3s 15 b) О 2-4 2-25 6 c) O 3 s 24 2-25 6 3 s d) O 2+25 3 5 15 e) O 2-4 (2-25) fONone of the above. Question 6 Find e2 sinh (5 x) 4 e cosh(5x) 2 а) О 2 (5 7) 2 (s3) 5 6 54 1 b) О 2 (s3) 2 (s 7) 54...
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 appli...
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...
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))...
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
hat would be the partition function of this system according to equa tion 7.16? (e) W (f) What is the probability of finding both particles in the same single-par state, for the three cases of distinguishable particles, identical bosons, ane identical fermions? 4) The entropy of a two-state para magnet is given by S = Nk [ln(2 cosh x )-x tanhx ]], where x 2 uB kT Find the value of S at T-0 and T-oo. sinhx = "(ex-c"); coshx-(ex...
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
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
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
5. (14,5) Here are some details about the function f(x) = cosh x. Use these details and the formula for Maclaurin series to find the Maclaurin series for f(x) = cosh x. Write out at least 6 terms of your answer and give your answer in summation notation f(x) = coshx f'(x) = sinh x f"(x)=cosh x f(0) = cosh 0 = 1 f'(0) = sinh 0 = 0 6. (12,4) In polar coordinates the graph of r = 7+7sin()...
Please do both of them. Thank you.
Find 3 cosh(2 x) 3 sinh(5 x)] 3 5 2+4 15 a) 225 3s 15 b) О 2-4 2-25 6 c) O 3 s 24 2-25 6 3 s d) O 2+25 3 5 15 e) O 2-4 (2-25) fONone of the above. Question 6 Find e2 sinh (5 x) 4 e cosh(5x) 2 а) О 2 (5 7) 2 (s3) 5 6 54 1 b) О 2 (s3) 2 (s 7) 54...
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...
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
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