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2. Use the theorem in Sec. 23 to show that f'(z) and its derivative f"(z) exist everywhere, and find f"(z) when (a) f(z) = iz + 2; (c) f(z)=z³; Ans. (b) f"(z) = f(z); (d) f"(z) = -f(z). (b) f(z)=e³e-iy; (d) f(z) = cos x cosh y - i sin x sinh y.

2. Use the theorem in Sec. 23 to show that f'(z) and its derivative f"(z) exist everywhere, and find f"(z) when (a) f(z) = iz + 2; (c) f(z)=z³; Ans. (b) f"(z) = f(z); (d) f"(z) = -f(z). (b) f(z)=e³e-iy; (d) f(z) = cos x cosh y - i sin x sinh y.

Calculus For The Life Sciences
Calculus For The Life Sciences
2nd Edition
ISBN:9780321964038
Author:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Publisher:GREENWELL, Raymond N., RITCHEY, Nathan P., Lial, Margaret L.
Chapter3: The Derivative
Section3.CR: Chapter 3 Review
Problem 59CR
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J(z)=e¹e-¹y. 2. Use the theorem in Sec. 23 to show that f'(z) and its derivative f"(z) exist everywhere, and find f"(z) when (a) f(z) = iz + 2; (c) f(z)=z³; Ans. (b) f"(z) = f(z); (d) f"(z) = -f(z). (b) f(z)= exe-iy; (d) f(z) = cos x cosh y- i sin x sinh y.
Transcribed Image Text:J(z)=e¹e-¹y. 2. Use the theorem in Sec. 23 to show that f'(z) and its derivative f"(z) exist everywhere, and find f"(z) when (a) f(z) = iz + 2; (c) f(z)=z³; Ans. (b) f"(z) = f(z); (d) f"(z) = -f(z). (b) f(z)= exe-iy; (d) f(z) = cos x cosh y- i sin x sinh y.
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