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MATA29H3 Lecture Notes - Lecture 7: Kinda Funny, Multiplication Sign

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26 Sep 2018

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MATA29H3 verified notes

MATA29H3 Lecture 6: [MATA29H][Lecture 06] - [Properties of Limits]

MATA29H3 Lecture Notes - Lecture 7: Kinda Funny, Multiplication Sign

MATA29H3 Lecture Notes - Lecture 8: Difference Quotient

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[mata29h][lecture 03] - [limits and touching on continuity] Continuation of last lectures examples about limits: c. 1) find lim x 1 x 1 f = lim lim. L (x) where x x 1 2 3 x{ 2 5 } 1 x 1 f = lim lim x 1 2 f (x) gets closer to. W e just substitute any number that s close to [1] from the negative side of the x et s try 0. 999? (0. 999) So, as we get closer to 1 from the left, the limit of x 1 f = lim lim. L x 1 + x2 5 x 1 f = lim lim eft side limit = ight side limit x 1 (1. 001)2 5 = 3. L c. 2) find lim x 1 x 1 g = lim lim. L (x) where x x 1 2 3.

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Related Questions

Show transcribed image text This Question: 1 pt 12 of 44 (0 complete) This Quiz: 44 pts possible Verify Property 2 of the definition of a probability density function over the given interval. ffx) 22x What is Property 2 of the definition of a probability density function? O A. The area under the graph of f over the interval [a,bl is b O B. The area under the graph of f over the interval [a.b] is 1 O C. The area under the graph of f over the interval [a,b is a. Since the given interval. [0.oo), has a right-endpoint of infinity, the area under the graph of fwill be calculated using an improper integral. Choose the correct formula for an improper integral over the interval [a,ool below t(x) dx= lim | f(x) dx= lim [F(x)]a= lim (F(b)-F(a)) b-o0 f(x) dx = lim | f(x) dx = lim [F(x)]-lim (F(a)-F(b)) b- 00 b--0o f(x) dk- lim x) dx- lim [F(x)m (F(b)-F(a)) b-+00
O D. 00 f(x) dx= lim f(x) dx= lim [F(æ£´= lim (F(a)-F(b)) b--oã Substitute a and b into the left side of the formula from the previous step and express the integral as a limit. area 2edx lim2edx Next, determine F(x). First, find the antiderivative of f. 2(Use C as the artbitrary constant.)
Next, determine F(x). First, find the antiderivative of f. as the anbliay cosat) Let C 0 in the expression obtained above and let the resulting expression be F(x). Evaluate the result over [0,oo) using the far right side of the formula for the area. area = As b approaches oo, e approaches infinity where c is a constant. Use this fact to calculate the limits from the previous step area+1 Is Property 2 of the definition of a probability density function over the given interval now verified? Choose the correct answer below A Property 2 o the definition o a probability density unction over the given interval has been ver ed since the expression in the previous step simplifies to o B. Property 2 of the definition of a probability density function over the given interval has not been verified because the expression in the previous step does not simplify to the expected area value. Â° C. â D Property 2 ofthe definition of a probability density function over the given interval has been verified since the expression in the previous step simplifies to 0 Property 2 o the definition o a probability density unction over the given interval has been ve ned since the expressio n e evious ste si plifies to 1.

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Please answer numbers 2c, 3a, and 3b. Please and thank you.