lim x-->0 tan3x/tan2x = 3/2 - have to write out the algebraic steps needed to discover that this is = 3/2.

I don't get math of why we break this out into (sin3x/cos3x)/(sin2x/cos2x), then times it by 1/2x and 3x, etc....just seems like there should be an easy way to think about extracting the 3/2.

### Want to see the full answer?

Check out a sample Q&A here*arrow_forward*Check out a sample Q&A here

*star_border*

## Related Calculus Q&A

Find answers to questions asked by students like you.

Q: 2 cos(8x) – 8 x² – 2 lim - sin(3x) — 2? — За

A: Here we apply l Hopital's rule.

Q: lim (x approaches 0) of [sin(5x)cos(6x)]/(x)

A: Click to see the answer

Q: ating / * sin (2x)cos(2x) dr by substitution, if u= sin(2x) th

A: Click to see the answer

Q: cOs x tan x 28) lim sin 3x 29) lim x→0 2x x3 + 2x2 + x 30) lim x→-1 x4 + x3 + 2x + 2 x3 – 2x2 + 4x –…

A: Click to see the answer

Q: -sin^2(x)=cos(2x) from [-pi, pi]

A: Click to see the answer

Q: 2ェ+ COS lim エ→ー 3.x - Vz?+3

A: I=limx→-∞2x+cosx3x-x2+3dividing x b N and…

Q: a. Solve for real x, in the equation sinh 2x – 2 cosh 2x + 2 = 0. b. Express tanh x in terms of e*…

A: Click to see the answer

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: 2 cos(4x) – 4x? – 2 - - 8. lim x→0 sin(2x) – x2 – 2x -

A: Topic = Limits

*question_answer*

Q: Evaluate sin 0 – 1 lim 0 - T/2 In sin 0

A: Click to see the answer

*question_answer*

Q: 7x cos()-7x [sin(-2x)sin(5x)sin(7x)] – lim 2x cos(x) lim x-0 5x?

A: Click to see the answer

*question_answer*

Q: 1-cos 2x sin² x limx-0

A: Since you have posted multiple questions, as per our policy we will answer first question. Please…

*question_answer*

Q: lim as x approches 0 of cos(6theta)-1/sin(7theta)

A: Given: fθ=limθ→0cos6θ-1sin7θ Apply limit by substituting θ=0 in the above expression.…

*question_answer*

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

A: Click to see the answer

*question_answer*

Q: tion for sin x= 0.3

A: Click to see the answer

*question_answer*

Q: 2 cos(5x) – 5 x² – 2 sin(3x) – x2 – 3x - lim - - (Write your answer in the given box)

A: Click to see the answer

*question_answer*

Q: Determine the following limits analytically.

A: limx→0 3tanx - 8x3x + sin2xlimit = ?

*question_answer*

Q: lim, (5 イータ 1-Sint Cos C)

A: Click to see the answer

*question_answer*

Q: 8. if y =; sinh(2x + 1) 9. ſ cot* 0 de. 10. * if y = cot-()- tan-1x.

A: Click to see the answer

*question_answer*

Q: 7x cos х -7x - lim [sin(-2x)sin(5x)sin(7x)] 2x3cos(x) lim 5x2 х>0

A: Click to see the answer

*question_answer*

Q: lim x→0 (sin10(x)cos(8x))/x=?

A: Click to see the answer

*question_answer*

Q: Hello, I need help with my homework question. Can you please show steps and details for me to…

A: Click to see the answer

*question_answer*

Q: Why is arctan(0) equal 0. Tan of 0 is 0 because sin0/cos0=0/1. So that makes tan (0)=0. But arctan…

A: Click to see the answer

*question_answer*

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

A: YOU SHOULD SPECIFY QUESTION NUMBER . WE CANNOT DO THIS MUCH QUESTIONS IN A SINGLE QUESTION. Limit…

*question_answer*

Q: EX-15- Prove that : a) Sec-'x= Cos- ! b) Sin-' (-x)=-Sin-'x

A: Click to see the answer

*question_answer*

Q: Solve sin 2x + cos x = 0 for 0 ≤ x < 2π.

A: Click to see the answer

*question_answer*

Q: Use an identity to solve the equation on the interval [0, 2π).

A: the given equation is: sin2x cosx+cos2x sinx=22 we have to solve the equation using the identity.…

*question_answer*

Q: 3x²+x d (sin-()+sec='(x) (1) Compute lim cot-1(3x+*+1) (ii) Find- X+00 3x2-7 dx tan-1x+tan-1

A: i).…

*question_answer*

Q: 1. cos (- x) - sin (- x) -- sin (주-x) TT =-1

A: Given cosπ4-x-sinπ4-x=-1 We know the identity cos(a)-sin(a)=2sina using this we will get…

*question_answer*

Q: If tanh(x) = 24, find the values of the other hyperbolic functions at x. sinh(x) %3D cosh(x) coth(x)…

A: Click to see the answer

*question_answer*

Q: Solve the equation on the interval 0s0<2n. 3 tan 0+ 1 = 0 What are the solutions to 3 tan 0+ 1 = 0…

A: Click to see the answer

*question_answer*

Q: If cos(x) = - and sin(y) = - with tan(x) > 0 and cos(y) < 0, algebraically compute the exact value…

A: Click to see the answer

*question_answer*

Q: Using Newton's method, the approximation of the root x of f(x) = 2 – x² – co within 10 starting with…

A: Click to see the answer

*question_answer*

Q: Find f'(x), if f(x)= tan² 4.x. Find f'(x), if f(x) = sin² 2x./cos 2x . Find f"(x), if f (x)= Inx+…

A: Click to see the answer

*question_answer*

Q: Compare the accuracies of the approximations sin x = x and sin x = 6x/(6 + x2) by comparing the…

A: Given: The approximations . The functions and

*question_answer*

Q: tanx 4 – lim 0 Cos[1– –] X 0.7 O 1.5 O 0.5

A: Click to see the answer

*question_answer*

Q: 10. What is the solution to the equation tanx+3 sec x +3 = 0 over the domain 0° <x < 360°? A. 60°…

A: Click to see the answer

*question_answer*

Q: How do I solve the limit as x goes to 1 for the expression (sin(3x-3))/(1-x) without using…

A: Rewrite the given expression as follows.

*question_answer*

Q: cos 2x +1 sin 2x Prove that Please show proper steps sin 2x 1- cos 2x

A: Click to see the answer

*question_answer*

Q: 3 2): If sinh(x) ;find tanh(4x). 4

A: Click to see the answer

*question_answer*

Q: - sin(-x) = and tan(-x) = cos (-x) =

A: we have to the given blank statement. sin(-x)=____________ cos(-x)=___________ tan(-x)=___________

*question_answer*

Q: solve for x if tan 3x = 5 tan x ( short cut way)

A: Click to see the answer

*question_answer*

Q: Solve sin r = cost exactly on 0 <I< 27. Choose one NOTE: Enter the exact, fully simplified…

A: Click to see the answer

*question_answer*

Q: A) By using simple Iterative method, find one root of the equation sin x = Use 3D. %3D (x2- In x)3

A: We have sinx=1x2-lnx3 Now, if we need to find a solution of fx=0 then we write fx=0 in the form x=gx…

*question_answer*

Q: =) lim cos 3x sec 7x Xー

A: 1) a) The given function is, limx→π2cos 3x sec 7x. limx→π2cos 3x sec 7x=00 Rewrite the given…

*question_answer*

Q: On the graph of f(x)=tanx and the interval [−2π,0), for what value of x does the graph meet the…

A: To Determine: What value of x does the graph meet the x-axis. Given function is :…

*question_answer*

Q: If tanh(x)=5/13, what is the sinh(x)?

A: Answer is sinhx=5/12. Explanation is given below..

*question_answer*

Q: In estimating / cos(2æ)dæ using Trapezoidal and Simpson's rule with n = 8, we can estimate the error…

A: Given function is, ∫-16cos2xdx For n = 8.

*question_answer*

Q: Prove the Identity

A: Click to see the answer

*question_answer*

Q: Is sin-1 x the same thing as1/sin x?

A: Click to see the answer