Question 9: Given that z = cos+ i sin and u- iv = (1+z)(1 − j²z²). Show that 30 2 V = utan r = 4² cos² (2) 3 wherer is the modulus of the complex numberu + -iv.

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Q: Let f(2)=u+iv be an analytic function. Given that u=v² show that f(z) is a constant.

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Q: (a) = √2+isin 2 (b) = (1+1)(cos+ i sin ) (c) zn = "+(-1)"

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Q: Which of the functions have 5 in their domain: f(x)=x²-3x

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Q: Q.5 Consider the Sturm-Liouville problem d -(xy')+(2-1)y=0, dx y'(1)=0, y'(e²)=0

A: Given,           xddxxy'+λ-1y=0,    y'(1)=0, y'(e2)=0.

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Q: 3. (Areas of Surfaces of Revolution). For each of the following subproblems: (a) sketch the…

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Q: prove V injective if x1 ‡xn → v(x1) = v(xn)

A: Solution:-

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Q: the following statement. 'If yes, explain why. If no, provide a counterexample. For every real…

A: If the function is injective , then the above statement is true.

Q: Find the bounded solution of au Əx = 2 อน at + U_if_U(x, 0) = 6e-³x. 1

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Q: prove v(x1) = v(xn) → x1 injective if x1 ‡xn → v(x1) ‡ v(xn) v →x1 = xn ⇒

A: To prove: vx1=vxn→x1=xn⇔x1≠xn→vx1≠vxn

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Q: Q.5 Consider the Sturm-Liouville problem d x(xy')+(2-1)y=0, dx y'(1)= 0, y'(e)=0

A: Given,                  xddxxy'+λ-1y=0,       y'(1)=0, y'(e2)=0