2³ + a² + 1 The value of lim sin ") i i rª + 5 Select one: O a. -1 O b. 0 c. None of the these O d. 1

Q: B. Verify the given identity is true. You m -1+tan 0 tan (135° + 0) 1+tan 0 Paragraph 4 ^ñ I

A:

Q: pef. Find lim, - o[cos(-)+2xsin(=). )+2xsin(=)). A O 1. BO .C O does not exist D O

A: Limit of the function

Q: az Q4: If z = tan-), then this form [ az + y 0] is correct? ду The form is correct. O The form is…

A:

Q: 06. Evmlete the integral 7sin (a)+ 7sin(2)tan? (x) de secz (x)

A: Integrated by substitutions

Q: Q: Prove the following identitie: (1+tan A tan B) +(tan A - tan B)* = sec' A sec' B.

A:

Q: Which of the following has the same graph as r = 1 - cos u? r = -1 - cos u

A: Given graph :  r = 1 - cos u and r = -1 - cos u

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: (a) Prove that, if n> 1 is a natural number. then tan"-(r) /- tan" (r) dr. tan" (r) dr n- 1 Use this…

A: Prove that ∫tannxdx=tann−1xn−1−∫tann−2xdx

Q: -t 2 lim 8 cos t ||

A: Given  The limit is limt→π2t2-π2t8cos t

Q: lim n(1- cos-) = in Select one: a. 3 b. 1 С. О d. 2 OO O

A:

Q: n: (1) lim sin(1/n") 1/ns n+00 (2) lim 21 etin

A: 1. if limx→0sinxx=1limn→+∞sin1n81n8=1

Q: 1. Prove the following identities: (a) secx – cos x = tan x sin x (b) sin(x + y) sin(x – y) = sin? x…

A: To prove:- sec(x) - cos(x) =tan(x) sin(x)  Sin(x+y) sin(x-y)=sin2(x) - sin2(y)

Q: Using the definitions: sin(z) = (e^iz - e^-iz)/ zi  and cos(z) = (e^iz + e^-iz)/z Prove that  sin…

A: Using the definitions: sin(z) = (eiz - e-iz)/ 2i  and cos(z) = (eiz + e-iz )/2 We need to prove that…

Q: 7. a) Prove the identity tan r sin r sec z- cos r. b) State all restrictions for z. Your answer:

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Q: *6. lim cos r

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Q: 7. a) Prove the identity (cos2z) cos z sin z-2sin³ z b) State all restrictions for tan z. <= tan z

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Q: I am confused about this homework problem.

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Q: Prove: Use the De Moivre's Formula to Prove that for any n greater than or equal to 1 (1+i tan e)"…

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Q: | 1- coS I lim I>0 x In(1 ++r is Select one: 1. a. 4. 2. 3. 1. C. d. b.

A:

Q: 91. Let I, = | x" cos(x³) dx and J, = | x" sin(x²)dx. (a) Find a reduction formula that expresses I,…

A: We have to find a recursive / reduction formula for the given integral.

Q: please answer ty

A: Used L-hospital rule

Q: З cos(21) - 3 3 tan(t) 2 Prove the following identity: 2sin(21)

A:

Q: Using that for z E C, cos z = and sin z prove that 2i cos( (cos z - sin z).!

A: To prove the given one

Q: (b) lim (cos ()) I-1 COS

A:

Q: Use the figure to identify all angles between 0 and 2n satisfying the condition. tan (0) = V3 V3…

A: Given; Tan(thetha) = √3.

Q: 1. Find the domain and ronpe of the the followinp tunctions; a) cos(x-T) x+x-2 b) _1 c) イー+anx xペ-イ

A: as per guidelines, we will solve first question. 1. a) Given function is  fx=1cosx-π

Q: 2. Prove the identity: (1 + cot A - csc A)(1 + tan A + sec A) = 2

A: Write the trigonometric ratios in sinA and CosA.

Q: . Which of the following is equivalent to cot²0sin²0-1, cos 0+1 1-cos e A. cos 0+1 1-sec e В. sec e…

A: Given that, the expression is cot2θ sin2θ - 1cos θ + 1

Q: 2. Which of the following statements are correct? (a) If z = 1+ 0i = x € R, then the definitions of…

A:

Q: Can i get help with this problem step by step?

A: Firstly, we use the result 1-cos2x=2(sinx)^2 and then we divide numerator and denominator by thita

Q: Let m be a real number. Then 2(sin (mx) + cos (mx)) = mn 2(sin (mx) + cos (mx)) = n %3D The above is…

A: Given, m is real number.

Q: Show computations for the other 2 missing values sin 2(-0.001) sin 2(0.001) f(-0.001) = f(0.001) =-…

A: On solving this we will get

Q: m -1 :If tan A = n tan B and sin A = m sin B, prove that cos A = n -1

A: Given that  tan A=n tan B sin Acos A=nsin Bcos B ................equation 1 also given that  sin A=m…

Q: Can you please answer this question and show all of the steps and say the correct letter

A:

Q: > Example 3. Prove that sin? z + cos? z = 1. eiz 2 e2iz - 2+e- -2iz sin? , = Z 2i eiz + e e2iz + 2+…

A: We have top prove that sin2z+cos2z=1 We have,…

Q: How would this Calculus problem be solved?

A: Given -5cos(πx)≤h(x)≤x5-1x-1 Using the Sandwitch theorem of limit…

Q: XII D. Prove the following identities. 4. cos3a = 4 cos' a- 3cosa tan x+cotx 9. cotx-tan x = sec 2x

A: Given :

Q: tane – cot0 a. Prove 1 – 2cos?0 6. Show 1– 8sin?0· cos²0 = cos(40) | tane + cot0

A:

Q: Determine if the statement is possible for some real number z. sin t = z possible O not possible

A: We have to find out z

Q: Q if asinx Prove that a + bcos X y' = (a+ bcosx)? a cos+ b

A: Differentiate wrt x In problem, proof equation is wrong I have solved properly

Q: +1- 2 cos 0 for Z E C., show z"+ = 2 cos(n@) that %3D

A:

Q: 14.6.9. Show that lim sin(a? + y²) dA(x, y) = |æ|,]y|<n I sin(a? + y?) dA(x, y) = 0. lim %3D…

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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: The value of the limit x→0 of (cos x)^(cot2 x) is 1.36 -1.36 2.7 -1 O O O

A: Given: y=limx→0(cos x)cot (2x)(1∞ form)⇒ln y=limx→0cot (2x) ln(cos x)          =limx→0 ln(cos x)tan…

Q: The relations cosh(i t) = cos t and sinh(i t) = i sin t were discussed in the Excursion. Use these…

A:

Q: Evaluate the following limit. 7 cos t+ -7 e-t-1 sin 2t -i- 2t lim k 7t 31 7 cos t+ -7 e-t-1 sin 2t…

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Q: 2. Discuss the continuity the following finctions Sinx a) ços (TT-2x) b) enxtd) -2 c) ex-

A: The Continuity of given functions are given below in handwritten format

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

A: We have to check

Q: 1+sin(x) lim is p ritoc 9. O alon13 (A) 0 (B) 1 (C) 2 (D) TT 00

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.