1) Evaluate the following indeterminate forms. a) lim sin 8x cosec 7x

Q: evaluate using the Squeeze Theorem.

A:

Q: Show that 1 lim 00 cos 0

A:

Q: Use the addition formulas to derive the identities in Exercise

A: There are six trigonometric ratios those are sine, cosine, tangent, cosecant, secant and cotangent.…

Q: Which of the following is not equal to 1? tan x lim 3 sin x lim x→0 3x 1 sin lim 1 O All of the…

A:

Q: lim[1-sin x] 19. 0 3 lim(1 + sin x) 20. x→0

A: 19) limx-0[1-sinx]1/x 20) limx-0[1+sinx]3/x.

Q: 1. Verify the following identities. sec4 x - tan4 x 2 sec2 x - 1

A: We have given the identity

Q: Evaluate using the Squeeze Theorem. lim cos θ cos(tan θ) θ→ π/2

A:

Q: 5 cos 3x2-5 lim x+0 2 sin 8.x

A: Follow the procedure given below.

Q: n+1 Evaluate lim cos (x² )dr (and show all work)

A:

Q: Prove that the inequality|cos(x)|≥1−sin2(x) holds true for allx∈R

A: Given inequality is

Q: 1 Show that (tan-' x) : 1+x?

A: We use Trigonometry identities and inverse Trigonometry to solve this proof

Q: What is the value of * cosx + sin2x + 1 lim x² – 7²

A: what is the value oflimx→π cosx+sin2x+1x2-π2

Q: 1. Use the Second Fundamental Theorem of Calculus to evaluate COS dr.

A: Please see the explanation below

Q: tan x lim

A: Consider the limits:

Q: Graph f. g, and f + g on a com- mon screen to illustrate graphical addition. f(x) = sin 3x, g(x) =…

A: Given

Q: 20. Prove the following identity. Use proper form. sin (-x) cosx= sin2x_1 3.1 cot (-x)

A:

Q: Prove the following trig identities: tan 2x - 2 tan 2x sin²x = sin 2x b. sec² x-2 secx cos x + cos²x…

A: To prove a. tan2x-2tan2xsin2x=sin2x b. sec2x-2secxcosx+cos2x=tan2x-sin2x

Q: Which of the following yields an indeterminate form as x → 0+ ? x cos x tan x sec x O x tan x 1…

A:

Q: Find the limit of the trigonometric function .

A: We have to find the limit of the function: limx→06-6 cos x3 This is determinate form of limit so we…

Q: What is the value of cosx + sin2x + 1 lim x2 – 72

A:

Q: Prove that the inequality | cos(x)| ≥ 1 − sin2 (x)

A:

Q: Prove the following identities: a. sec(x - π/2) = cscx b. cscx-cosxcotx = sin x c. cos x/ 1+sinx +…

A: (a) The given identity.

Q: Evaluate using Theorem as necessary.

A:

Q: sin 3x lim x0 2x

A: Consider the provided expression, limx→0sin3x2x Find the limit of the following trigonometric…

Q: where m, n Evaluate lim X/2 cos nx +0 are integers.

A:

Q: Prove the following A. Secxtanx/tan^2x+1=sinx B.sin^2xcot^2x/1-sin^2x=1

A:

Q: Is the following indentity true? 1 1 2sec2 (x) 1+ sin(x) 1- sin(x)

A:

Q: 1. Verify that the following equations are the identity csc2 (-x) tan(x) cot(-a) - sec2 (r) a. %3D |

A: Given problem:-

Q: Use the fourth Maclaurin polynomial for cosx to approximate cos 12, cos

A:

Q: 2.6 Show that if J sin ! if 0 < x <1, if x = 0, f(x) = then lim,-0+f(x) does not exist. (See Fig.…

A:

Q: 2COTX Prove that Sin2x is an identity || csc2 x

A: we use the property of trigonometric function to shoe the result

Q: COS x tan x lim

A: Given: limx→0cosxtanxx

Q: Rewrite cos(arctanx) as an algebraic expression in x. (That is, express cos(arctan x) entirely in…

A: We know that tan is the ratio of opposite side to the adjacent side, and cos is the ratio of…

Q: Prove that c) 1-tan?A -Cos 2A Htan?A

A:

Q: Prove that sin x+ cos -1 -1

A:

Q: Use the identity sin 20 = 2 sin 0 cos e to evaluate lim sin 20 – 2 sin 0 | 02

A:

Q: PROVE that sin x = v1 – cos² x is NOT an identity.

A: Topic:- trigonometry

Q: 1. Prove the following identities. 1+cosx a) secx - tanxsinx = - b) sinx %3D cscx + cotx secx

A: 1(a). The given data is: To prove the identities: secx-tanxsinx=1secx

Q: Show that cos(x) >1 – x²

A: In this question, the concept of the Mean Value Theorem is applied. Applying Mean Value Theorem in…

Q: Prove that there is a real number r so that sin(r) = x – 1.

A: We have, sinx=x-1 Let us consider a function fx such that, fx=x-1-sinx

Q: Prove the following identities. sin 2x csc x =

A: Topic:- trigonometry

Q: Use the intermediate Value Theorem to show that the folowing equation has at least TWO distinct…

A:

Q: Evaluate using Theorem 2 as necessary.

A: Given, limt→0cost-costt Now by using the L-Hospital rule we get, ⇒limt→0-sint+2sint…

Q: Evaluate lim cos(sin 0) O -1 O 1 O does not exist

A:

Q: 7. Prove that lim r' cos(5/r) 0.

A: Topic = Limits

Q: sinax cos bx dx = 0

A:

Q: Prove the following using trig identities 2 tan x d) csc2X sec2x I3D

A: Given: 1csc2x=2tanxsec2x The objective is to prove the trigonometric identities,

Q: 6. Use the Intermediate Value Theorem to show that the following equation has at least TWO distinct…

A: Intermediate Value Theorem states that ''If a continuous function has values of opposite sign inside…

Q: Which of the following statements is NOT true? 1- cos(1) A 1-OL lim =0 B lim |=0 I+ sin(t) =2 (c)…

A: We can check the truthfulness of the given options as below

Q: Prove that cosx = x³ + x< +4x has exactly one root in [0,pi/2]

A:

Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.