Question

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.

Expert Solution
Check Mark
Blurred answer
Students who’ve seen this question also like:
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN: 9781133382119
Author: Swokowski
Publisher: Cengage
Not helpful? See similar books
Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
The Trigonometric Functions. 39E
marketing sidebar icon
Your question is solved by a Subject Matter Expert
marketing sidebar icon
Want to see this answer and more?
Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*
*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.
Get 24/7 homework help!
8+ million solutions
Get access to millions of step-by-step textbook and homework solutions
Support from experts
Send experts your homework questions or start a chat with a tutor
Essay support
Check for plagiarism and create citations in seconds
Solve math equations
Get instant explanations to difficult math equations
Students love us.
Students love us.

Related Calculus Q&A

Find answers to questions asked by students like you.

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

A: Click to see the 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

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…

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.…

Q: if sinh x=-1/2 then coth x is

A: Click to see the answer

Q: tion for sin x= 0.3

A: Click to see the 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

Q: Determine the following limits analytically.

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

Q: lim, (5 イータ 1-Sint Cos C)

A: Click to see the 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

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

A: Click to see the answer

Q: lim x→0 (sin10(x)cos(8x))/x=?

A: Click to see the 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

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

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…

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

A: Click to see the answer

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

A: Click to see the 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.…

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).…

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…

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

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

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

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

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

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

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

A: Click to see the 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

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.

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

A: Click to see the answer

Q: 3 2): If sinh(x) ;find tanh(4x). 4

A: Click to see the answer

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

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

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

A: Click to see the 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

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…

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…

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 :…

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

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

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.

Q: Prove the Identity

A: Click to see the answer

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

A: Click to see the answer

Knowledge Booster
Calculus
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
  • Algebra & Trigonometry with Analytic Geometry
    Algebra
    ISBN:9781133382119
    Author:Swokowski
    Publisher:Cengage
    Algebra and Trigonometry (MindTap Course List)
    Algebra
    ISBN:9781305071742
    Author:James Stewart, Lothar Redlin, Saleem Watson
    Publisher:Cengage Learning
    Trigonometry (MindTap Course List)
    Trigonometry
    ISBN:9781305652224
    Author:Charles P. McKeague, Mark D. Turner
    Publisher:Cengage Learning
  • Algebra & Trigonometry with Analytic Geometry
    Algebra
    ISBN:9781133382119
    Author:Swokowski
    Publisher:Cengage
    Algebra and Trigonometry (MindTap Course List)
    Algebra
    ISBN:9781305071742
    Author:James Stewart, Lothar Redlin, Saleem Watson
    Publisher:Cengage Learning
    Trigonometry (MindTap Course List)
    Trigonometry
    ISBN:9781305652224
    Author:Charles P. McKeague, Mark D. Turner
    Publisher:Cengage Learning