c. lim sinh r d. lim sinh x

Q: Evaluate the following limits.

A:

Q: Use the limit definition to compute f '(a) and find an equation of the tangent line.

A: Answer: f'(-2)=-1

Q: Find the limit (if it exists).

A: If the vector valued function is of the formr(t) = f(t)i + g(t)j + h(t)kThen its limit is given…

Q: Consider the function f defined by Sin (3x?) if x ±0 f (e) { 22 if ge =0 Use the limit definition of…

A: Consider the function  f(x)=sin(3x2)2x,          if x≠00,                       if x≠0

Q: Use the definitions of the hyperbolic functions to find each of the following limits. (If the limit…

A:

Q: Use the definitions of the hyperbolic functions to find each of thefollowing limits. limx→∞tanh x

A: We use the hyperbolic definition of tanh(x)

Q: Find the limit (if it exists).

A:

Q: Find the limit if it exists.(Use squeese Thcor lim Cx,y)>(0,0) x²+5y²

A:

Q: Find the limits

A: Given:

Q: Use the definitions of the hyperbolic functions to find each of the following limits. a. lim tanh x…

A:

Q: Use the definitions of the hyperbolic functions to find the following limit. lim 8sinhx X+- 0 а. 1…

A: The solution are next step is

Q: Find the following limits (if they don't exist write DNE, ∞ or -∞ as appropriate): lim(2x² – 3x).…

A:

Q: Use l’Hôpital’s rule to find the limits

A: We first rationalize the numerator.

Q: Find the following limit. Answer in either integer or fraction form. NO DECIMAL APPROXIMATIONS. If…

A: Use l hospital rule for finding the limit.

Q: Use the definitions of the hyperbolic functions to find each of thefollowing limits

A: e) The given limit is limx→∞sech x. As cosh (x)=ex+e-x2 and sech x=1cosh x thus substitute cosh…

Q: Determine the following limit, using o or - o when appropriate, or sta lim sec 0 01/2+ . ond GU in t…

A:

Q: Use the definitions of the hyperbolic functions to find eachof the following limits. limit x…

A: Consider the follow formula: tanhx=ex-exex+ex

Q: The following limit 9a? – 16y? - lim (x,y)→(0,0) 4у + За

A:

Q: Use the definitions of the hyperbolic functions to find eachof the following limits. limit x…

A:

Q: Use the properties of limits to calculate the following limit. x? + y³ lim 3 3 (х.у)-(1,2) х* - у x²…

A: We have to find

Q: Use l’Hôpital’s rule to find the limits

A: Given: limt→0sint2t To determine:  The value of given limit using L' Hospital's rule. Concept used:…

Q: Use l’Hôpital’s Rule to find the limits

A: Given: limx→π2-sec7xcos3x we know that  secθ=1cosθ so, limx→π2-cos3xcos7x  00 form it is 00 form, so…

Q: Use L'Hôpital's Rule to calculate the following limits. sin r + tanr 1² – 1 te (a) lim (b) lim Inr…

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

Q: Q2: Find the following limits 3. lim sin3y cot5y y-0 ycot4y

A:

Q: Find the limits in Exercis

A: Given: L=limx→0x-xcosxsin23x

Q: In r Т lim, 0+ 01 O II O III OIV O Not Indeterminate

A: Hee, the given expression is: limx→0+ln xx

Q: 1-cos r-r² 1) lim,-0

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

Q: Find the following limits (if they don't exist write DNE, ∞ or -∞ as appropriate): Answer: lim x-3 2…

A: We have given to find limit  Let ,  y=limx→3x2-2x-3x-3 y= limx→3x2-3x+x-3x-3 y= limx→3xx-3+1x-3x-3…

Q: Use L'Hospital's rule to determine the following limit. Use exact values. e1a – 1 4x lim x →0…

A: We apply L-hospital's rule, when we get 0/0 form.

Q: f(x, y) = e¬aY sin(x + y) (г, у) —> (1, -1). as

A: We will plug the limits in function to find limit of function

Q: (b). Compute each of the following limits. (i). lim,4 ". (ii). lim,0 tanz

A: For (i),     limx→ 4x2-x-12x2-4x=limx→ 4(x+3)(x-4)x(x-4)=limx→ 4x+3xPlug in the value x=4.=4+34=74

Q: Find the limits. Are the functions continuous at the point being approached?

A: We will find the limit by substitution

Q: Use the definitions of the hyperbolic functions to find each of thefollowing limits

A: Our Aim is to find the limit of the following expressions using the definitionof hyperbolic…

Q: Use l’Hôpital’s Rule to find the limits

A:

Q: Find the following limit. Answer in either integer or fraction form. NO DECIMAL APPROXIMATIONS. If…

A: To find the limit.

Q: Use the definitions of the hyperbolic function to find each of the following limits. lim x→∞…

A:

Q: Use the definitions of the hyperbolic functions to find each of thefollowing limits. limx→∞sech x

A: Given: limx→∞sech(x)

Q: Use the definitions of the hyperbolic functions to find each of thefollowing limits. limx→-∞sinh x

A:

Q: Use the definitions of the hyperbolic functions to find each of thefollowing limits. limx→0+coth x

A: Let the given limit be y - y = limx→0+cothxy = limx→0+coshxsinhxy = limx→0+ex+e-x2ex-e-x2y =…

Q: Determine whether the following limits exist either by giving a proof from first principles or…

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: Use the definitions of the hyperbolic functions to find eachof the following limits. limit x…

A:

Q: Find the following limits (if they don't exist write DNE, ∞o or -∞o as appropriate): Answer: lim h→0…

A:

Q: ) Determine whether the following limits exist either by giving a proof from first principles or…

A:

Q: Find the following limits. Do not apply L'Hospital's rule. 2-4 lim +2 x– 2| (1) (ii) sin²(3r) lim…

A: According to question given:(i) limx→2x2-4x-2When x approaches 2 from right x-2=x-2When x approaches…

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) lim (ti + sin(t)j +…

A: Given that lim rtt→π=limt→πti+sin tj+cos tk   If the vector is of the form rt=gti+htj+ftk Then, its…

Q: 1 – cos(x² + y?) x2 + y? - lim (x,y)→(0,0)

A: Given lim(x,y)->(0,0)1-cosx2+y2x2+y2 find out the limit if it exists

Q: cos t – cos² t Evaluate lim t→0 t

A: →When limit is of the form 00 or ∞∞, then L'Hospital rule is used.      In this rule take the…

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.