h(x) =  { tan^-1 (x^2+2x+1), if x is less than or equal to -1 [[x + 1]], if -1 < x < 1   (note: [[x + 1]] is a greatest integer function) coth^-1 (x), if x is greater than or equal to 1   Determine if h is continuous at x = −1, 0, 1. If not, identify if it is removable, jump essential, or infinite essential.

Q: L’Hôpital’s Rule is used incorrectly. Describe the error.

A: Given: limx→∞xcos1x

Q: solve using L'Hopitals Rule 6. Lim    (2tanx - sin2x) / x3   x->0

A: limx→02tanx-sin2xx3

Q: solve using L'Hopital's Rule 1. lim      [ 1/(sin^2 x) ]  - [ sinx/x^2 ]    x->0

A:

Q: Find the limit: x->0  2 sin2 3x / 3x2

A:

Q: Use L' Hopital's Rule to find the limit as x approaches positive Inifinity of:  ln(x)-ln(1+x) Hint…

A: Given ln(x)-ln(1+x)

Q: ln(x) is just defined for x greater than 1. Select one: True False

A:

Q: 16. etan (1) sec² (x) dr

A:

Q: 1-sinx x-1-cos2x 9) lim 10) lim TC X- sinx-cosx TL X- 4

A:

Q: 1 Only one of these calculations is correct to evaluate the limit lim sinhx, X+0 Select one: 1 lim…

A: We have to evaluate the following limit . I have explained in details please see the explanation and…

Q: lim tanx i. x→ 0 lim In(1+ x)] 11. x→ 0 lim sin ax i1. where a and b are constants. r0sinbxr

A: We are only allow to to do first question and three subpart of question So if you need rest of…

Q: ON 3 sec3(In x) + sec2(In x) tan(In x) 2х n x) tan(In x) n x) dx c³(In x) + sec²(In x)

A: We have to choose the correct option according to the given information

Q: Solve without L'Hopital's rule. lim x→1 [tan(1 − x)] / (2x^2 + x − 3)

A: We have to find out limit

Q: 1-cosx 16. lim X-0 3x sin x

A:

Q: JFNO Uie limit, USe THospital's Rule if appropriate. 6x + sin(x) x-0 8x+cos(x)

A:

Q: f(t) = In Itsinx 1-sin x g(x) = x sin ¹3x + √1-9x² G(x) = x In (9 + x²) + 6 tan-¹ (-)-2x

A: Note: Since, in the first function there is a typing error "f(t)", it should be "f(x)" because it is…

Q: Use L'Hopital's rule to evaluate lim(1 – 2 sinh(x)) sch(a).

A:

Q: lim x approaches 0   1-cos(x)/x2 please!!! don't use derivatives in the solution as I'm a beginner…

A:

Q: tan(1 – x) 2 limx→1 2x +x – 3

A:

Q: 1. f(cos 3x - x²) (sin 3x- x³)5 dx 2. f cos² x (tan x) (sec² x − 1) dx 3. f tan x (sec² x - 1)(sec²…

A:

Q: 1+ tanx log prove that = sec2x dx y 1- tanx

A: Giveny=log1+tanx1-tanx

Q: How to solve the limit of sin(x)•ln(x) as x approaches 0 from the right using L'Hopital's rule.

A:

Q: limit x to infinity (1+sin(3/x))^x

A:

Q: limit of x approaching 0 from the right of ((sin(x^2))^x )

A: Given   apply squeeze theorem

Q: lim * In(sec(2x)) x→0 (sin(3x))³

A: To find the limit.

Q: x2 cos x+sin2x Find the limit: lim by means of the L' Hopital's |x sin x X-0 Rule.

A: We need to find the limit: limx→ 0x2cosx+sin2xxsinx. So,              limx→ 0x2cosx+sin2xxsinx=limx→…

Q: Limit as x approaches 0 of Sin(5x)/(2x

A: Limit as x approaches 0 of Sin(5x)/(2x

Q: Compute the derivative of Sin x in two ways: (i) Using the chain rule. (ii) Taking the derivative of…

A:

Q: sin(4x) lim x→0 sin(8x)

A: To find the given limit

Q: しx)f erentiate f メて ×ケ-X arcsin (3x -1)+ In (5x*+3) 6arctan (1-x) . メ9 fon

A: f(x) = sin-1(3x-1) + ln(5x4+3)

Q: Use : L'Hospiral's Rule lim In x X-o ot cot x

A: We have to find limit of given function.

Q: 1 Only one of these calculations is correct to evaluate the limit lim sinhx x-0 Select one: (1 lim…

A:

Q: x+1 1-x In [cosh (x+1) + sinh (x+1) lim 2tanh x=1- lim_ In x=1+ l

A:

Q: Find the limit as x-->0 of sin(-3x)/sin(2x)

A:

Q: f(x) = = x, over the interval - < x < and has period 27 f(x) [cos cosz+cos3z + cos 5 +... f(x)…

A:

Q: prove that cosh^2x-sinh^2x=1

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Use Mean Value Theorem to show that ln(1+x) 0

A:

Q: solve using L'Hopital's Rule 2. Lim      (x-sinx) / (x^3)    x->0

A: To find: The limit of limx→0x-sin xx3. Calculation: Apply L'Hospital rule: limx→0x-sin…

Q: solve using L'Hopital's Rule 7. Lim    1/(tan-1)2  -  1/x2    x->0

A: Given the limit as : limx→0 1tan-12-1x2 We need to find the limit by using L' Hopital's Rule. Let's…

Q: solve using L'Hopital's Rule 3.  Lim    (ex + e-x  - x2 - 2) / (sin2x - x2)    x->0

A: L'Hopital's Rule: The rule is applicable when the value of the limit function limx→af(x)g(x) is…

Q: 2 sin x lim In

A:

Q: Limit Sin 1/x x -0

A: Answer is mentioned below

Q: Use the L' Hopital rule to solve: lim x->0 2sinx-sin2x/x-sin x

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: 1 - cosh x lim x→0+ ln(x² + 1)

A:

Q: 1. lim sin x sin 2x x-0 1-cos x 3x+x+2 . lim X-4x3+8x+1

A: d) To evaluate                       limx→0 sin x sin 2x1- cos x                            =sin (0)…

Q: 2x² + x + 3 x³ + x dx In[x] + In (x² + 1) + tan^³(x) + C Option 1 3 In]x] +In (x² + 1) + tan¹(x) + C…

A:

Q: Limit x approaches to minus infinity under root 5-x

A: Property used: limx→∞f(x)=limx→∞f(x) Some properties of ∞: ∞+a=∞∞b=∞∞=∞

Q: 1 (sinx\1-cosx lim X→0

A: We need to evaluate limx→0sin xx11-cos x Let y = sin xx11-cos x Then log y = 11-cos x log sin x…

Q: tan(x)-sin(x) e. lim x2 tan(x) (In (cos(3x))] f. lim 2x2 tan(x)-x g. lim x0 (sin(x)-x. ex-In(1+x)-1…

A: e) Given data:   The expression for the given limit is limx→0tan(x)-sin(x)x2tan(x).     The given…

Q: Find delta value for the limit of x-->0 of tan5x/sinx when epsilon = 0.1

A: Introduction: The limit of a real-valued function is the base of differential calculus. A single…

Q: (1) limx→(π/2)-(tan x) (2) limx→0 x ³(tan-¹ x - x)

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…