# is the limit as x approaches 0 of sin3x over 3x equal to zero? sorry-- basically this is my problem: lim [sin 3x / 4x) x-> 0 ~~~~I multiplied& eventually got to .75* lim (sin 3x / 3x) x-> 0

19,187 results
1. ## Math

Which describes the end behavior of the graph of the function f(x)=-2x^3-5x^2+x? a. f(x) approaches infinity as x approaches negative infinity and f(x) approaches infinity as x approaches infinity b. f(x) approaches negative infinity as x approaches

2. ## Math (Limits)

What is the limit of g(x)=x as x approaches pi? Would it just be pi??

3. ## Calculus

Determine whether the sequence converges or diverges. If it converges, find the limit. (If an answer does not exist, enter DNE.) limit n approaches infinity of an = e^(−6/sqrt(n))

4. ## Calculus

Let f be a function defined for all real numbers. Which of the following statements must be true about f? Which might be true? Which must be false? Justify your answers. (a) lim of f(x) as x approaches a = f(a) (b) If the lim of f(x)/x as x approaches 0 =

5. ## Math

If the limit as x approaches 1 for (f(x) - 7)/(x-1)=8, evaluate the limit as x approaches 1 for f(x)

6. ## calc bc (condensed

is the limit as x approaches 0 of sin3x over 3x equal to zero? sorry-- basically this is my problem: lim [sin 3x / 4x) x-> 0 ~~~~I multiplied& eventually got to .75* lim (sin 3x / 3x) x-> 0 ~so i figured since (lim (sinx/x) x-> 0 was equal to zero, then

7. ## Calculus Limits

Question: If lim(f(x)/x)=-5 as x approaches 0, then lim(x^2(f(-1/x^2))) as x approaches infinity is equal to (a) 5 (b) -5 (c) -infinity (d) 1/5 (e) none of these The answer key says (a) 5. So this is what I know: Since lim(f(x)/x)=-5 as x approaches 0,

8. ## limiting position of the particle

A particle moves along the x axis so that its position at any time t>= 0 is given by x = arctan t What is the limiting position of the particle as t approaches infinity? Answer is pi/2 How do I solve this? Thanks a lot. You want to find the limit of

9. ## calculus

A state charges polluters an annual fee of \$20 per ton for each ton of pollutant emitted into the atmosphere, up to a maximum of 4,000 tons. No fees are charged for emissions beyond the 4,000-ton limit. Write a piecewise de nition of the fees F(x) charged

10. ## Calculus

Find the limit lim as x approaches (pi/2) e^(tanx) I have the answer to be zero: t = tanx lim as t approaches negative infi e^t = 0 Why is tan (pi/2) approaching negative infinity is my question?

11. ## Calculus

Our professor wants us to evaluate the limits analytically without using a table or a graph, and if it doesn't exist we must describe the behavor near the limit point. I'm not sure how to evaluate each side of a limit separately without looking at a table

12. ## Calculus

What is the limit of the following equation? Limit as x approaches infinity of ((e^x) - ln(x)) / (x^3)

13. ## Calculus

the limit as x approaches 3 from the right of ln(x^2 -9). what is the limit, if it exist?

14. ## math Help ASAP

write and solve inequality 17. the speed limit of a highway is 55 miles per hour. a car is traveling at least 65 miles per hour. how many miles per hour m over the speed limit is the car traveling? A 55-m>equal to 65;m. eqaul to 10 B m+65< equal to 55; m <

15. ## Math

f(x) = cos (1/x) Find the limit as x approaches infinity and find the limit as x approaches negative infinity. Identify all horizontal asymptotes.

16. ## calculus

Which of the following best describes the limit as x approaches 4 of the quotient of 2 times x divided by the quantity negative 2 plus square root of x ? It exists and equals 4 It fails to exist because it is unbounded. It fails to exist because its

17. ## Calculus

1. Evaluate the function at the given numbers (correct to six decimals places). Use the results to guess the value of the limit,or explain why it does not exist. F(t)=( t^(1/3) - 1)/(t^(1/2) - 1) ; t= 1.5,1.2,1.1,1.01,1.001; The limit of F(t) as t

Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim f(x) as x approaches 3, where f(x)= x^2-8x+9 if x/3 (greater than or equal to 3)

19. ## Calculus

Evaluate the limit using algebraic techniques. limit of (x^2 - 25)/(x^2 - 4x - 5) as x approaches 0. How do I do this?

20. ## calculus

Suppose h(x) = f (g(x)) and the graphs of f and g are shown below. Describe the continuity of h at x = 0. how would you do this if you were given two graphs: discontinuity at -2,0; point at -1,1; and point at 0,0 (to make a parabola) then discontinuity at

21. ## Calculus

Find the limit Limit as h approaches 0 of : SqRt(4+h)-2 ____________ h by relating it to the derivative. (Indicate reasoning.)

22. ## Algebraic limits

The limit as x approaches infinity. (1)/(5^x) The limit as x approaches 1. (1-x^3)/(2-sqrt(x^2-3)) Show your work thanks in advance!

23. ## Calculus

The table below gives selected values of a twice differentiable function f(x) x|. -7. -6. -4. -2. f(x)|. 0. -1. -2. 0 f'(x)|. 3. 2. -1. 7 What is the limit of f(3x-1)/(x^2)-4 as x approaches -2? What is the limit of f(f(x))/5x + 20 as x approaches -4?

24. ## Calculus 3

Find the limit, if it exists, or show that the limit does not exist. lim of x+y/y^2-x^2 as (x,y) approaches the point (-1,1).

25. ## calculus

The limit as x approaches 0 of ((4^x)-1)/x The limit above represents the derivative of some function f(x) at some number a. Find f and a.

26. ## Math - Limits

Find the limit of f(x) as x approaches 0. f(x) = [1-cos^2(3x)] / x^2 Is there a way to do this if we haven't learned L'Hopital's rule yet? Can we rewrite 1-cos^2(3x) as sin^2(3x), and then use the basic limit: lim x→0 sin(x) / x = 1? Thank you!

27. ## Math >> limits

find limit : lim (3sin4x / sin3x ) x--> 0

28. ## Calculus

Determine the limit of the trigonometric function: Limit as x approaches pi/4 of (1-tanx)/(sinx-cosx) I need step by step help using the special trignometric limits theorem.

29. ## Calc: Limits

how to calculate the limit: *I got confused especially with the square root. 1. lim as x approaches 2 (squareroot x^2 +5)-3 / (x-2) 2. lim as θ (theta) approaches zero (tan^2 (5θ) / (sin (3θ) sin (2θ) )

30. ## Calculus

1. Use the Taylor series to calculate the limit. Problem: limit as x approaches 0 is equal to (1-cos(x))/(1+x-e^x). I did the problem out but I need help in seeing if its correct. limit as x approaches 0 is equal to (1-cos(x))/(1+x-e^x)=

31. ## calculus

find the limit of f'(x) = 1/(√x) using the limit definition of derivative as x approaches 0.

32. ## limits

what is the derivative of e^(3*ln(x^2)) i keep getting 6/x * e^(3*ln(x^2)) but that's not one of the multiple choice so am i doing something wront. also, what is the limit of (1-cosx)/(2*(sinx)^2) as x approaches zero. is the answer zero or nonexistent The

33. ## Pre-Calc

Determine the one sided limit of f(x) s x approaches -2 from the right side. F(X) = (x^2-2x+4)/(x^3+8). I do not know where to begin. Should I plug in the one side limit?

34. ## calculus

The fee per ton of pollution is given by A(x) = F(x)=x. Write a piecewise de nition of A(x). What is the limit of A(x) as x approaches 4,000 tons? As x approaches 8,000 tons?

35. ## Maths

Prove By induction that sinx + sin3x + sin5x +.... Sin(2n-1) =sin^2(nx)/sin3x

36. ## limit from graph

How do I know if the limit of a function exists or not from that function's graph. Thanks. It the graph of a function becomes straighter at + and -infinity, it means that the function behaves linearly in the limit. However there may be other types of

37. ## Math: Limits

Estimate the limit numerically. lim as x→(approaches to)5 6e^(x − 5) How do I solve it? I don't plug in the numbers do I? Then how do I do this as well? What should I do to solve lim x→(approaches to)− infinity 6xe^(7x) Do I disregard the other

38. ## Calc- Limits

what is the limit of x as it approaches 1 when x/ln x?

39. ## Calculus

In the interval (0 is less than or equal to x which is less than or equal to 5), the graphs of y=cos(2x) and y=sin(3x) intersect four times. Let A, B, C, and D be the x-coordinates of these points so that 0

40. ## Math

I've got quite a few problems. Please answer any of them in whole or in part. Thank you in advance. (For the record, you're not doing my homework; you're helping me understand it. These problems were not assigned.) (1). Determine the discontinuities and

41. ## Differential Calculus

use the rule that says limit of (e^h - 1)/h = 1 as h approaches 0 to show that the limit of [ln(x+h)-lnx]/h as h approaches 0 = 1/x, where x>0

42. ## Integration?

Sorry, i have a load of questions on integration... thanks for any help provided! Evaluate the integrals: limit 0 to pi/4 ∫ [sec^2x]/[5+tanx] dx limit 0 to pi/6 ∫ [3cos3x]/[3+sin3x] dx limit 0 to 3 ∫ [2x-1]/[x^2-x+1] dx

43. ## Calculus

How can I find the horizontal asymptote of: y=e^x/(2e^x+5) i know you have to do the limit as x approaches infinity... but that is about all i know... mulitply the numberator and denominator by e^-x y= e^0/(2e^0 + 5e^-x) y= 1/(2 + 5e^-x) now, take lim as x

44. ## physiology

Assume that fluid enters the distal convoluted tubule with an osmolarity of 100 mOsm and that the maximum osmolarity of medullary interstitial fluid is 1100 mOsm. As plasma ADH levels rise, the osmolarity of the urine a) approaches 300 mOsm, the normal

45. ## math

evaluate the limit as x approaches 0 from the right. of the function xcos(1/x) I know the answer is O but I am not sure as of my reasoning. I just that that since cos(1/x) is being multiplied by a number approching 0 that the whole limit would be o.

46. ## Math

A particle P starts at the origin (x0,y0)=(0,0), of the plane. The particle moves in steps as follows. 1. P moves 1 unit to the right to the point (x1,y1)=(1,0), then 2. P moves 1/2 unit up to (x2,y2)=(1,1/2), then 3. P moves 1/4 unit to the left to

47. ## Calculus

Find the limit limit as x approaches 1 of (2-x)^3tan[(pi/2)x]

48. ## Calculus

Determine whether the sequence (-1)^n(n/(n+1)) diverges or converges. I think it diverges because the limit as n approaches inf. of n/(n+1) is 1, and the limit of (-1)^n does not exist.

49. ## calculus

The fee per ton of pollution is given by A(x) = F(x)=x. Write a piecewise de nition of A(x). What is the limit of A(x) as x approaches 4,000 tons? As x approaches 8,000 tons?

50. ## Calc

True or false: a) if f(x) is continuous at a, then the limit of f(x) as x approaches a exists b) if the limit of f(x) as x approaches a exists, then f(x) is continuous at a My answer: a) false b) true

51. ## calc bc

is the limit as x approaches 0 of sin3x over 3x equal to zero? thank you!

52. ## Calculus

What is the limit of this function as x approaches 0? cos(x) - 1 / x From what I gather, the limit is equal to 0, since on the right, the function approaches from negative values close to zero and on the left, it approaches 0 with positive values close to

53. ## Calculus

Give an example of a function f which is defined at c which limit as x approaches c of f(x) exists, but that limit does not equal f(c).

54. ## Calculus

Could someone please help me with these questions;I was having trouble with these four questions. Evaluate each limit, if it exists, using any appropriate technique. 1.) The limit as u approaches 4; u^2-16/u^3-64 2.) The limit as x approaches 1; x^3+

55. ## Math

F(x) = x^2 +1 , x cannot equal 2 F(x)= 3 , x=2 What is the limit of f(x) as it approaches 2?

56. ## Differential Calculus

use the rule that says limit of (e^h - 1)/h = 1 as h approaches 0 to show that the limit of [ln(x+h) -lnx]/h as h approaches 0 = 1/x, where x>0

57. ## calculus

use the rule that says limit of (e^h - 1)/h = 1 as h approaches 0 to show that the limit of [ln(x+h) -lnx]/h as h approaches 0 = 1/x, where x>0

58. ## Calculus- limits

f(x) = x + 7 if x < or equal to 5 F(x) = 7 if x >5 what is the limit as x is approaching 5 from the left side????? I know that the limit as x approaches to 2 does not exist and that the limit as x is approaching 5 from the right side is 7

59. ## Calculus

Determine the limit as x approaches 1 f(x) if f(x)={3-x, x does not equal 1 and 1, x=1 A. 2 B. 1 C. 3/2 D. DNE E. None of these

60. ## math

How to solve for delta using trig functions? i.e. cosine sine tangent secant Thank you I'm not sure what delta you're referring to. Could you please elaborate some for us. What is it you're trying to do with the trig funtions? the problem is.. limit sec

find the limit: lim of f(x) as x approaches 1 if f(x) = x^2 + 4, x is not equal to one and 2, x = 1. What is the answer and why?

62. ## Calculus

Determine the behavior of limits A. Limit as x approaches 1 of: (log x)/((x-1)^2) B. Limit as x approaches infinity of: ((x-1)^2)/(log x))

Evaluate the limit: Limit as x approaches 6 from the right: Sq.root of (x - 6). I know the limit is 0, but how do I show this? Thanks in advance.

64. ## Calculus

Find limit as x approaches 1 5/(x-1)^2 A. 0 B. Negative infinity C. 5/4 D. Infinity If I use limit as h approaches 0 f(x+h)-f(x)/h , will I get an x in the answer?

65. ## Math

f(x) = cos (1/x) Find the limit as x approaches infinity and find the limit as x approaches negative infinity. Identify all horizontal asymptotes.

66. ## maths

If (e^x)(sin3x)=Im ((e^x)(e^i3x)) integrate (e^x)(sin3x) I get the answer(e^x)(cos3x-3sin3x) +C My book gets the answer (1/10)(e^x)(sin3x-3cos3x)+C Can any explain which answer is right and why Integral of e^(1+3i)x = e^(1+3i)x /(1+3i) + c Multiplying

67. ## Math-Calculus

Hi, I am trying to figure out what the limit as h approaches 0 of (1-2h)^(1/h) is. I am unfamiliar with the process I am supposed to use to solve this limit. I have just been reasoning out this limit, but I keep getting the answer, 1^(infinity)=1. My

68. ## Calculus

In First principles there is usually a part that states as lim approaches 0. Now I came across a question where the limit was as 1 approaches 3. what should I do?

69. ## math

Find the limit of the function: (tanp)(x-1)/(tanq)(x-1) as x approaches 1. We're hinted at using the result that sinx/x = 1 as x approaches 0. Im not sure how we go abt doing this qs. thanks in advance

70. ## Calculus

Is there a number "a" such that the limit as x approaches -2, f(x) approaches (3x^2+ax+a+3)/(x^2+x-2) exist?

71. ## Calculus 3

Find the limit, if it exists, or show that the limit does not exist. lim of x+y/y^2-x^2 as (x,y) approaches the point (-1,1).

72. ## Calculus

Another one I'm not sure about is the limit as x approaches infinity of (x^2)/lnx I took the derivative of the top and bottom and got 2x/(1/x) which is the same thing as 2x^2. Can I keep going or do I just say that the limit does not exist?

73. ## Calculus

Evaluate the following limit. lim e^(tanx) as x approaches the righter limit of (pi/2)

74. ## Math Help Plz

By graphing estimate to two decimal places the following limit.What is the limit of f(x)=(1+x)^(1/x)as x approaches 0

75. ## Help with one limit

I'm asked to find the limit as n approaches infinity of : [(2^(n) +1]/ [2^(n+1)]. The review we were given has [1+ 2^(-n)] / 2 as the next step, but I'm not quite sure how to make that leap myself. The final answer is 1/2. How do you solve this limit?

76. ## Calculus

Evaluate the limit. The limit as x approaches 0 of (x-sin(x))/(x-tan(x))

77. ## Calculus

So this one is confusing me: limit of n as it approaches infinity of (n{SIGMA}i=1) (1/(2^i) *the n is on top of the sigma notation and i=1 is at the bottom. I understand that 'i' would equal (n(n+1))/2 however the algebra from there confuses me.

78. ## Caculus

Find the limit of f(x)=1/(x-1) as approaches 1 think inifnite limit

79. ## calculus

Find the limit limit as x approaches 1 of (2-x)^3tan[(pi/2)x]

80. ## Calculus part 3 so sorry

y = e^2xsin3x Find the derivative. So I used the product rule and I got sin3x(e^2x)+cos^3x(e^2x). But the actual answer is sin3x(2e^2x)+cos^3x(3e^2x) Where the the 2 and 3 before the e come from?

81. ## Math

I am supposed to figure out what this rational function is by using these clues and I am a little confused. Can someone please explain how I do this? asymptotes: horizontal~none vertical~x=-4 slant~y=x+1 end behavior~ f(x) approaches infinity as x

82. ## calculus

What is the limit of the function as x approaches infinity? (x^4 - 7x + 9) / (4 + 5x + x^3) From what I know, the limit should be infinity since the greater exponent is in the numerator. However, I am only given the options: 0, (1/4), 1, 4, or Does not

83. ## calculus

Suppose that f(x) is bounded: that is, there exists a constant M such that abs(f(x)) is < or equal to M for all x. Use the squeeze theorem to prove that lim x^2f(x)=0 as x approaches 0. if g(x) is Mx^2 then what is f(x) and h(x) according to the squeeze

84. ## Calculus

I am sorry. I am really struggling with limits. I am not sure of an answer for this problem either: Show an example that the limit as x goes to a f(x) goes to [f(x)+g(x)] may exist even though neither the limit as x goes to a f(x) approaches f(x) or g(x)

85. ## Trigonometric

sin3x=(sinx)(3-asin^2x) Wow! is that arcsin^2(x) ??? are we solving for x? or is it proving the identity? proving the identity sin3x=(sinx)(3-sin^2x) Your identity is wrong, it should say: sin3x=(sinx)(3-4sin^2x) try this: sin(3x) = sin(2x + x) = sin2xcosx

86. ## Maths

given (e^x)sin3x = Im((e^x)(e^i3x)) Integrate (e^x)sin3x.dx You can just take the imaginary part of the integral of ((e^x)(e^i3x))= e^([3i +1)x] which is IM(3i +1)e^(3ix + x) = IM (3i +1)e^x*e^(3ix) = IM {(3i +1)*e^x* [ cos (3x) + i sin (3x)] = e^x* sin

87. ## Calculus

True or false: a) if f(x) is continuous at a, then the limit of f(x) as x approaches a exists b) if the limit of f(x) as x approaches a exists, then f(x) is continuous at a My answer: a) false b) true

88. ## Calculus

How do I find the limit of (1+sin(pi times x))^(1/x) as x approaches 0? I tried using wolframalpha, but am unable to understand their steps. My thinking is that you set y=the limit and use L'hopital's rule a couple times. The answer I got was y=e^0--->y=1,

89. ## Psychology

"I just can't make myself study ahead for a test. I work better under pressure. Perhaps it is the fear associated with waiting until the last minute that gets me going." This approach to motivation is best explained by: A. incentive approaches. B.

90. ## Calculus check

The limit as x approaches 1 (x^3-1)/(x^2-1) is I got 3/2

91. ## Calculus

what is the limit of x/(ln x) as x approaches 0?

92. ## calculus

limit as x approaches 1 x^2-4/x-1

93. ## Calculus

What is limit as x approaches 0 of x*(2^x)/((2^x)-1))

94. ## Math

Limit as x approaches 0 √5+x - √5/x

95. ## math

limit of x approaches -3. (2x^2 + 4x + 1)

96. ## math

first question: could x^5-1 simplified? what is the limit of cuberoot(x^2-5x-4) as x approaches 4? For the first one: could x^5-1 simplified? Yes, the expression can be factored as the 5th roots of unity. First, divide it by (x-1) to get (x^5-1)=(x-1)*4th

97. ## Psychology

"I just can't make myself study ahead for a test. I work better under pressure. Perhaps it is the fear associated with waiting until the last minute that gets me going." This approach to motivation is best explained by: (Points: 5) incentive approaches.

98. ## Calc Limits

lim (1+x)^1/x. Give an exact answer. x->0 This reads: The limits as x approaches zero is (1 plus x) to the 1 divided by x. The log of each term is (1/x) ln (1 + x) = ln (1+x)/x Using L'Hopital's rule for the limit of f(x)/g(x), the limit if the log is lim

99. ## Calculus

(2x + sin x)/x What is the limit as x approaches zero?