Verify the identity algebraically. Use a graphing utility to check your result graphically. (Simplify at each step. tan?(0) sec(0) = sin(8) tan(0) tan²(0) - (( D/cos(0) )tan(e) = sin(8) tan(8) sec(0) 1/cos(0)

Q: Verify the identity.

A: Here we have to verify the identity,

Q: Simplify tan (-x) ese(x) cos(x)= А. О В. 1 С. -1 D. sinx

A: tan(-x) cosec (x) cos (x) = [Sin(-x)/ cos(-x)] cosec (x) cos(x)  = [sin (-x)/cos (x) ] cosec (x) cos…

Q: lim cos(@) - 1 sin(@)

A:

Q: 4. sin2 -x | dx. Use trigonometric groups. 2 X| cos

A:

Q: 11 csc2 (-0) tan 0 cot(-0) Establish the identity: - sec2 e

A: Given,

Q: tan(tan3x)dx Evaluate: cos-3x -In |sec (tan3x)| + C (B ® - in [cos(tan3x)| + C © - sin( tan3x)| + c…

A: We need to evaluate the following integral I = ∫tantan3xcos23xdx…

Q: cos x-cos(5x) Prove identity: tan(2x) sin x+sin(5x)

A:

Q: sin - COS I Q1-Solve by hospital rule lim

A: By using L hospital rule

Q: simplify sin x-1/cos x - cos x /sin x-1

A: The given expression is

Q: cos( – x) + tan( – x)sin( – 2)

A:

Q: 1 lim x? sin 1-cos³ x lim X→0 sin² x csc? x-2 lim п cotx-1 4

A: L'hospital rule: If limx→cf(x)g(x)=00 or ∞∞, then limx→cf(x)g(x)=limx→cf'(x)g'(x). Limit formula:…

Q: if sinh x=-1/2 then coth x is

A:

Q: 1- sin0 lim а) 1+ cos 20 2

A:

Q: A. Let 0 = 2x, then the identity cos 2x = 1-2 sin2 x becomes cos e = 1–2 sin2 (0/2). a. Use this…

A:

Q: 1-cos(2x) sin²(3x) tan x-sin x Evaluate: a- limr-0* b- lim sin³x

A: (a) Given, Simply fie the above expression, On applying the limit, the solution is in 0/0 format.…

Q: Verify the identity: tan(-x)cos x = -sin x

A: To verify:      tan(-x)cos x = -sin x We will start from LHS and will try to get RHS.

Q: 1+sin(2x) 6) Prove the trigonometric identity = 1+ sec(x) csc(x) sin(2x)

A:

Q: 2. By hand, showing all steps, determine sin 4x sin 5x lim x sin 3x

A:

Q: Verify the identity algebraically. Use the table feature of a graphing utility to check your result…

A:

Q: 1-cos(2x) - Evaluate: a- lim,-0 sin²(3x) tan x-sin x b- lim sin3x

A: According to L'hopitals rule,limx→af(x)g(x)= limx→af'(x)g'(x)iff(x)g(x)= 00or ∞∞. If there is any…

Q: 1- cos () 1- cos(x) 1- sin°(;) 1+ cos(x)

A:

Q: Evaluate the limit.

A:

Q: how do I solve this problem ?lim x-0 1-cosx/cos^2x-3cosx+2

A: First we use substitution property of limit, and that's given an undetermined form.Then we use…

Q: tan e 2. Find the domain of the function f:0→. 2 sin e-3 cos e

A: Domain for any function fθ is defined as the real values for θ for which fθ exists. The given…

Q: X 1 sin x+sin 2x Q3/ Find the value of (x) if 5 -2 1= lim %3D 3x -1 2 1

A: We will seperately find the determinant and the limit. Then, we will equate them to solve for x.

Q: An algebraic expression equivalent to the one below: sec[arcsin(x-1)]

A: Answer and explanation is given below

Q: Simplify sin(tan^-1(x/2))Simplify sin(2tan^-1(x/2))

A: according to given information we have to find different partspart-1

Q: ex-e2 1. lim x→2 x-2 x2 2. lim X0 sin 5x2 3. lim 5 cos 3x2-5 sin 8x2

A:

Q: 6. (a) Express cos (2 tan- ) (b) Express sin (2 cosx) as an algebraic expression in x. (c) Express…

A:

Q: sin a COS T Solve by hospital rule lim-

A: after solving we get limit is 1/3

Q: The root of sin x - (1 /3) x = 0 close to x = 2.2. %3D

A: We have to find the root of sinx-13x=0 close to x = 2.2.

Q: (1- cosx) cosx) limx-0 - ? x sin(x2) %3D

A: We have to find the value of limit

Q: cos x – 1.75 = -1 COS X sin(4x) = 2 – sin 4x 4 tan(2x) – 1 = 3

A:

Q: cos x cot x 1 csc x - 1 - sin x 4.

A:

Q: find x sin-1(1-x)-2sin-1x=90 degree

A: sin-1(1-x)-2sin-1x=90 degree

Q: 1 - cos2 x/sin x

A: To simplify the expression.

Q: lim 1-cosx/sinx ? x-->0

A: Given:

Q: 2x tan -1 I + COS (b) lim

A:

Q: cOs x tan x 28) lim x→0 sin 3x 29) lim x→0 2x x3 + 2x2 + x 30) lim x→-1 x4 + x3 + 2x + 2

A: As per our guidelines we need to solve only 3 questions .please repost the remaining subparts as…

Q: cos2x – sin2x cos2x x=-F(x)+c•What is F(x)? For = - sinr

A:

Q: x sin æ+tan² I lim, 0 1-cos

A: We can solve this as follows:

Q: • tan°(x) Xp- cos“(x) 1 1 tan9

A:

Q: 4. lim sin2ß B-0 sin3ß

A:

Q: cos x (1 + tan² xr )

A:

Q: sin(4.x) Find lim 1-0 tan(2x)

A:

Q: given tanx= -3/4 and 0*<x<180* , find the exact value of cos(x/2)

A: To solve the following problem

Q: ´1-cos x 1-cos³ 11. lim sin? x

A: The given data is limx→01-cos3xsin2x Here we use L-Hospital's rule and the L-Hospital's Rule states…

Q: Verify the identity algebraically. Use the table feature of a graphing utility to check your result…

A: 2sin x-2csc x=2 csc x-2 sin x

Q: Find the limit.

A: We have to find the limit: limθ→0cos θ-1sin θ This is 00 indeterminate form so we can apply L'…

Continuous Probability Distributions

Probability distributions are of two types, which are continuous probability distributions and discrete probability distributions. A continuous probability distribution contains an infinite number of values. For example, if time is infinite: you could count from 0 to a trillion seconds, billion seconds, so on indefinitely. A discrete probability distribution consists of only a countable set of possible values.

Normal Distribution

Suppose we had to design a bathroom weighing scale, how would we decide what should be the range of the weighing machine? Would we take the highest recorded human weight in history and use that as the upper limit for our weighing scale? This may not be a great idea as the sensitivity of the scale would get reduced if the range is too large. At the same time, if we keep the upper limit too low, it may not be usable for a large percentage of the population!