(d) Does lim f (x) exist? If it exists, what is x→3 the value? (e) Is the function f(x) continuous at x = 3.Justify your answer.

Q: . Does the existence and value of the limit of a function ƒ(x) as x approaches c ever depend on what…

A:

Q: Find the slope of the tangent line to the parabola y=4x-x^2 at the point (1,3) 1) using the…

A: Given

Q: Find the limit, if it exists.

A: The limit of a function limx→Xfx=Y means that value of  function f(x) can be as close to Y by making…

Q: Find the value of the limit lim SINX X 0 2x 02x (a) 0 (b) 1 (c) 1/3 (d) 1/2 (e) 1/4

A: Here we have to find the limit of the function. In the first step use the property of the limit:

Q: Plot the graphs of u(x) = 1+ |x – and I(x) = sin x on the same set of axes. What can you say about…

A: Sandwich theorem of limit states that if our original function is sandwiched between two functions…

Q: You are given that a function f is differentiable on (-o, 0), and that lim f'(x) = 6. lim (f(x + 3)…

A: Use the mean value theorem and calculate limit in following way:-

Q: lim 4 sin(x + n) + 3

A:

Q: b) Find two functions such that lim, 0 f(x) = 0 lim, 0 g(x) = 0 but lim, 0 f(x)g(x) = 1

A:

Q: Evaluate the limit.

A: We have to evaluate the following limits- limh→0sin4h4h

Q: 16. Find the equation of the line tangent to the functionf (x) = 6Vx at x-4. *hint: use lim,a…

A:

Q: Let lim,-0+ f(x) = -2, where 8r - 3 for r <0 f(x): | 4x – 2 for r2 0 f(r) = Then what is (the…

A:

Q: lim (sin?x x-0 x2

A: We use L-Hospital Rule to evaluate this limit.

Q: Find the limit of the transcendental function. lim x → T/2 4 sin x

A: Definition of limits helps to find the limit of the given function. The value is said to be the…

Q: Evaluate the limit: sinx lim x→0 e4x – 1

A:

Q: find the limit of g(x) as x approaches the indicated value.

A: Concept: The calculus helps in understanding the changes between values that are related by a…

Q: If lim f"(x) = +00, then the trapezoid estimation Tn - f(x) dx O TRUE OFALSE can never be within…

A: Given,

Q: Evalute the lim sin5x/x(x-1) as x approaches 0.

A:

Q: -1, x0 c. lim f(x), where f(x) =

A:

Q: Evaluate the limit. lim     In (Sinh x)x →0+

A: we have to evaluate the limit. lim     In (Sinh x)x →0+

Q: Use the graphs of f and g and their tangent lines at (-1,0) to find f(x) lim Number x-1 g(x) y f(x)…

A:

Q: Use the Squeeze Theorem to prove lim = 0. x00 x+ e- For x 0, since 0 < e* <1, we have

A:

Q: 8-3x, for x <1 For parts b) and c), let f(x)= %3D x+x, for x21' b) lim f(x) x→1

A: We have to evaluate  limx→1- f(x) For x &lt;1 , f(x) = 8 - 3x

Q: Let f(x) = 3x² – 5x + 1 f(x+h)-f(x) (a) Find f'(x) using the limit definition of derivative. That…

A:

Q: t. Find f' (x) = lim,→0 f(x+h)-f(x) for f (x) = Vax

A: We have to find the derivative of given function using first principle of differentiation.

Q: Evaluate the limit.

A: We have to evaluate the limit: limh→0sin 9hh We know that limx→0sin xx=1 So making same angle of…

Q: If lim f"(x) = +0o, then the trapezoid estimation Tn - | f(x) dx %3D x0* can never be within 10¯³ of…

A: Given that limx→0+f''(x)=+∞ And Tn≈∫01f(x)dx Error for trapezoidal method contains double…

Q: Consider the function: f (x) · g (x) = 16x · sin What is lim f (x) · g (x)?

A:

Q: Find the limit: lim, 0+ x(ln x)²

A: The given expression is: limx→0+x(ln x)2 Which is in 0×∞ form. So, convert it into ∞∞ form.…

Q: Show that xy lim (x,y)→(0,0) x2 + y8 does not exist.

A: If two different path have two different limit then limit does not exist . Now find the limit along…

Q: Does the existence and value of the limit of a function ƒ(x) as x approaches c ever depend on what…

A:

Q: x - 2x What is wrong with applying L'Hôpital's Rule to lim x+0 3x – 2

A:

Q: Find the limit. x² + y® sin х - у +7 lim (x.y)→(0,0)

A: Given,

Q: Suppose that f(x) is a differentiable function (with a continuous derivative), such that f(0)=f'(0)…

A:

Q: Find the limits limx→0+x (ln x)2

A: Consider : limx→0+x(ln2x). Modify the limit function. limx→0+(ln2x)1x…

Q: f(2) is continuos if lim f(z) =f(z,)

A:

Q: Find the limits limx→e+(ln x)1/(x-e)

A: Limit:      x→e+limln x(x-e)=h→0limln (e+h)(e+h-e)

Q: 4. lim f (x)=4, where c is any real number エー mil lim[ f(x)" a.

A: Given limx→cfx=4, where c is any real number. To evaluate: limx→cfx3 Solution: Power rule of limit…

Q: The graph of a function f and its tangent line at 0 are shown. What is the value of lim X→0 e7x f(x)…

A:

Q: Find the limits: x² – x - а. lim x→1 In x e* – 1 b. lim x→0 sin x .3 c. lim С.

A: Limits using L'Hospital Rule

Q: If lim f"(x) = +0, then the trapezoid estimation Tn - | f(x)dx x0* can never be within 10-³ of the…

A: Given that limx→0+f''(x)=+∞ And Tn≈∫01f(x)dx Error for trapezoidal method contains double…

Q: (b) lim log1 r+2+ (x – 2)? sin(2x2 – 3x – 2),

A: solution:-limx→2+ log13x-22sin2x2-3x-2=limx→2+ -log3x-22sin2x2-3x-2=limx→2+…

Q: True and False. (1) _A function f is continuous at x = a if and only if limf(x) = f(a). y=x² -10x+5…

A: (1) Concept : A function is continuous if the graph of the function is continuous or we can make the…

Q: Find the limit by interpreting the expression as an appropriate derivative. e2x lim- 1 i X0

A: As we already know that, dydxx=a=limh→0f(a+h)-f(a)h

Q: -x + 1, x > 0 3) Let f(x) = sin x -,x < 0' (a) Find left-hand and right-hand limits as "x"…

A: we have given f(x).  We have to find the left hand and right hand  limit.

Q: Evaluate the following limits.

A:

Q: If x Vx sf(x)s -x+ 1for all positive x-values, then what is lim f(x)?

A:

Q: (2+h)* Use the definition of the derivative to evaluate lim h+0 h

A:

Q: f(0) = 1, f"(x) < 0 for x # 0, lim f'(x) = +0, lim f'(x) = -00

A:

Q: ,if x> -3 Given the function f(x) =' 3 ,ifx S-3 is continuous at x=-3

A: A function                      fx=x2-9x+3,   if x&lt;-33,             if x≤-3 We have to answer 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.