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p(z)= q(z) = 1 ² 1/2 2=0 : 0<<2 B x=2 1+ sin((-2)): 2<x<4 : 0≤r <1- = r 2 x=1 -1+√√√x-1: 1<x<4 2<2=4 Which of the following statements are true? (select all that apply) Diff:[0,1]→R is continuous on [0,1] then it is Riemann integrable on [0,1]. sinh is continuous on Reven, and periodic cos achieves a global maximum at one or more x-values, is periodic, but has no second derivative. Every definite integral is also an indefinite integral. tanh is differentiable on its domain, odd, and has a horizontal asymptote. True or False: The function f(x)=√x(x-1) x € (0,0). is a polynomial (in x). O True False Let g: R→R be an even function, and let h:R→R be an odd function. Consider the following two statements: Statement : sinh(g(x)) XER is even. Statement Ill: sinh(h(x)); XER.is even. Statement is necessarily true but not Statement II. O Neither statement is necessarily true. Statement il is necessarily true but not Statement 1. Both statements are necessarily true. if g: R→R achieves a global maximum at CER and h:R-R is an decreasing function then: Ohog achieves a global minimum at g(c). Ohog achieves a a global maximum at g(c). Ogoh achieves a global minimum at c Ohog achieves a global minimum at c. This question is about the function q(x) in the question paper (see the rough diagram and the piecewise formula). This function achieves a global maximum at which of the following x-values (select all that apply, could be more than one) 0₂ None. 01 4 q(b) The most effective way of applying the change of variables formula (g(x))q'(x) dx = h'(u) du to the integral ["6x² sin(x³) dx is to q(a) take hi(u) = 6cos(u) O 2sin(u) O-cos(u³) Let g: R-R be a periodic function, and consider the following two statements: Statement: g(√x) XER. is periodic. Statement il: tanh(g(x)). XER. is periodic. Neither statement is neccesarily true. Statements I and il are both neccesarily True. O Statement is neccesarily true but not Statement. Statement is neccesarily true but not Statement II. iff:R-R is a decreasing function and g:R-R is an increasing function, then the composition fog is: O increasing. O decreasing constant. O Cannot be determined based on the given information. This question is about the function p(x) in the question paper (see the rough diagram and the piecewise formula). We are using the definition of local extrema as presented in WTW153, which allows endpoints as possible local extrema. This function achieves a local maximum at which of the following x values (select all that apply. could be more than one 25 3.5 None. 0 4 Let f:1-3,7]-R be a function and nE (2,3,4...). Let Let A- the numbers A. B and C. OBSCSA AsBsC O ASC sB O CSBsA O Cannot be determined based on the given information. 10(-3+101) 8-10 (-3+10/-13) an B= n +10(1-1)) and C= f(x)dx-0 n Order p(z)= q(z) = 1 ² 1/2 2=0 : 0<<2 B x=2 1+ sin((-2)): 2<x<4 : 0≤r <1- = r 2 x=1 -1+√√√x-1: 1<x<4 2<2=4 Which of the following statements are true? (select all that apply) Diff:[0,1]→R is continuous on [0,1] then it is Riemann integrable on [0,1]. sinh is continuous on Reven, and periodic cos achieves a global maximum at one or more x-values, is periodic, but has no second derivative. Every definite integral is also an indefinite integral. tanh is differentiable on its domain, odd, and has a horizontal asymptote. True or False: The function f(x)=√x(x-1) x € (0,0). is a polynomial (in x). O True False Let g: R→R be an even function, and let h:R→R be an odd function. Consider the following two statements: Statement : sinh(g(x)) XER is even. Statement Ill: sinh(h(x)); XER.is even. Statement is necessarily true but not Statement II. O Neither statement is necessarily true. Statement il is necessarily true but not Statement 1. Both statements are necessarily true. if g: R→R achieves a global maximum at CER and h:R-R is an decreasing function then: Ohog achieves a global minimum at g(c). Ohog achieves a a global maximum at g(c). Ogoh achieves a global minimum at c Ohog achieves a global minimum at c. This question is about the function q(x) in the question paper (see the rough diagram and the piecewise formula). This function achieves a global maximum at which of the following x-values (select all that apply, could be more than one) 0₂ None. 01 4 q(b) The most effective way of applying the change of variables formula (g(x))q'(x) dx = h'(u) du to the integral ["6x² sin(x³) dx is to q(a) take hi(u) = 6cos(u) O 2sin(u) O-cos(u³) Let g: R-R be a periodic function, and consider the following two statements: Statement: g(√x) XER. is periodic. Statement il: tanh(g(x)). XER. is periodic. Neither statement is neccesarily true. Statements I and il are both neccesarily True. O Statement is neccesarily true but not Statement. Statement is neccesarily true but not Statement II. iff:R-R is a decreasing function and g:R-R is an increasing function, then the composition fog is: O increasing. O decreasing constant. O Cannot be determined based on the given information. This question is about the function p(x) in the question paper (see the rough diagram and the piecewise formula). We are using the definition of local extrema as presented in WTW153, which allows endpoints as possible local extrema. This function achieves a local maximum at which of the following x values (select all that apply. could be more than one 25 3.5 None. 0 4 Let f:1-3,7]-R be a function and nE (2,3,4...). Let Let A- the numbers A. B and C. OBSCSA AsBsC O ASC sB O CSBsA O Cannot be determined based on the given information. 10(-3+101) 8-10 (-3+10/-13) an B= n +10(1-1)) and C= f(x)dx-0 n Order
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Statistics The Art and Science of Learning from Data
ISBN: 978-0321997838
4th edition
Authors: Alan Agresti, Christine A. Franklin, Bernhard Klingenberg
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