1 2. Let: f(x):= (x - 2)2 – 31 (a) Discuss domain of definition and image...
complex analysis 6. Let z" f(z)=lim 1 z (a) What is the domain of definition of f, that is, for which compiex numbers z does the limit exist? (b) Give explicitly the values of f(2) for the various z in the domain of f. 6. Let z" f(z)=lim 1 z (a) What is the domain of definition of f, that is, for which compiex numbers z does the limit exist? (b) Give explicitly the values of f(2) for the various...
please solve the question 13. a) Find the inverse of the function f(x)=cosh x=2(c+e-x) b) State the domain and range of both the function and its inverse. Determine if the series is absolutely convergent, conditionally convergent or divergent. 14. o 5(-1)" In n 1/2 13. a) Find the inverse of the function f(x)=cosh x=2(c+e-x) b) State the domain and range of both the function and its inverse. Determine if the series is absolutely convergent, conditionally convergent or divergent. 14. o...
Problem 1. Consider the function f(x)- 3.12 show that f is Riemann integrable on [0.2] and use the definition to find .后f(x)dr Problem 2. Consider the function -2, zEQ 2, O f(r) = Show that f is not Riemann integrable on 0,1 but s Reemann integrable on this interval. Problem 3. (a) Let f be a real-valued function on a, b] such thatf()0 for all c, where c E [a, b Prove that f is Riemann integrable on a, b...
(2) Consider the function f given by f:R R f(a)1 2 (a) Determine the domain D and range R of the function f. (b) Show that f is not one to one on D. (c) Let ç D be a subset of the domain of f such that for all x ? S, 0 and the function is one to one. Find such a set S. (d) For the set S given in Part (c), find f (x) (e) Determine...
Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t 2 0. Then the integral 2{f(t)} -6° e-str(t) dt is said to be the Laplace transform of f, provided that the integral converges. Find L{f(t)}. (Write your answer as a function of s.) {f(t)} = (s > 0) f(t) (2, 2) 1
let f(x)=ln(x)x>0 let k(x)= f(g(x))and m(x)= f(g(x))a) Find the domain of the function K(x).b) Find the domain of the function M(x).c) Find the value of k'(5)
1) Let f(x)=9x-2;g(x)=under square root 3x+7. Find each of the following. A) domain of (f+g) B) domain of fg C) domain of f/g (my answer is all r real number am i right?) 2) Let f(x)=3x-2;g(x)=5x+1. Compute the indicated value. A) (fogof)(2) i don't get the answer.please help me. Thanks
4. (a) Indicate where the series is (i) absolutely convergent, n-1 where it is (ii) conditionally convergent, and where it is (iii) divergent. Justify your answers Find f,(z) if f(x) = arctan (e* ) + arcsin V2x + 4. (b) (a) Set up (but do not evaluate) a definite integral that represents the area 5. of the region R inside the circle r = 4 sin θ and outside the circle r = 2. Carefully sketch the region R. (i)...
2. Let 6 marks (a) Find f(x),f"(x), and f"(x). (b) Find the second order Taylor expansion of f at 1, namely f(r) = ao + ala-1 ) + a2(z-1)2 + R2(x), where Ra is the remainder. You should find ao, a, a2, and R(p). 8 marks that the error in this estimation (i.e., R2(0.9)1) is at most 10-3. 6 marks (c) Use the Taylor expansion found above to estimate the value of f(0.9). Show Find f(x), f"(), and f" (b)...
4. [20 points] Let f(x) = 4 – 22. (a) Find an approximation to the integral and n= 3. $ f(x) dx using a Riemann Sum with right endpoints (b) Use the definition of a definite integral (with right endpoints) to calculate the value of the n(n+1) integral 2 $* f(x) dx. Hint: Ži= i=1