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# (a) State and prove the theorem giving the Weierstrass M-test. You may use the Cauchy convergence criterion without proof:(b) Consider the functional series Li ...

## Question

###### (a) State and prove the theorem giving the Weierstrass M-test. You may use the Cauchy convergence criterion without proof:(b) Consider the functional series Li (c â‚¬ (1,0)) J=] Given the information that the functional series (*) is pointwise convergent, show that it is uniformly convergent on [@, 0o) for each (ii) Show that the formally differentiated series (obtained by differentiating term by term) is uniformly convergent on [a,0) for each You may use without proof the inequality j Fa /

(a) State and prove the theorem giving the Weierstrass M-test. You may use the Cauchy convergence criterion without proof:  (b) Consider the functional series Li (c â‚¬ (1,0)) J=] Given the information that the functional series (*) is pointwise convergent, show that it is uniformly convergent on [@, 0o) for each (ii) Show that the formally differentiated series (obtained by differentiating term by term) is uniformly convergent on [a,0) for each You may use without proof the inequality j Fa / log j < where exp(1) ea (iii) Use the results of and to show that the function ((z) Lj  (c â‚¬ (1,00)) is continuously differentiable-  #### Similar Solved Questions

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Review Pant A A parallel-plate capacitor is formed from two 3.5 cm diameter electrodes spaced 0 mm apart The electric field strength inside the capacitor is 2.0 X106 N/C You may want to review (Pages 644 - 645) What is the charge (in nC) o each electrode? Express your answer using two significant fi...
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