2t Q3. Find the value of: lim,-0 tant (x² -1 Q4 Let f(x) ={ 2kx x< 2 x 2 2 Find the value of (k) that makes the function is continuous at x = 2.

Q: (2 cosh z, sinh z, 2 0. Then the lim f(x) A does not exist B is 2 C is 1 D is 0 B

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Q: Q2) find the value of each limit sint 1) lim(- 1+cost +tcost C+cost x+xcosx 2) lim 0 sinxcosx

A: The limits of given functions are given as follows :

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Q: 0: A- Find the limit for the following functions: - 1- lim tan2x X0 sin4x 4x-3 3r-9x²+x-3 3- lim 2-…

A: Givenjn

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Q: Find the value of the limit below. [4 – 6(x + Ax)]? – (4 – 6x)² - lim Ax → 0 Дх Specify the function…

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Q: 2.r + y Find lim (x,y)→(0,0) 2.x²y + xy² or show that it does not exist.

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Q: Along the path z= e find 2. lim (2,4)→(1,0) y-4zy 3x-y-3

A: Here, we have to reduce this limit to a limit in a single variable by using the equation of curve.…

Q: xy Let f(x, y) : and let L = lim(2,y)>(0,0) f(x, y). Which of the 8x2 + 9y2 following statements is…

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Q: Based on the given values, is the function continuous or not? If not, select the condition which is…

A: In the given question we have to tell such function which satisfies the given three property and and…

Q: O:: A- Find the limit for the following functions: - tan2x 4x-3 3x3-9x²+x-3 1- lim x→0 sin4x 2- lim…

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

Q: ) Find the value of k that makes function continuous at ¤ =4 f(x) = { | 2x +7 > 4 6x -k < 4 (i) If…

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Q: Q 4. (a). Simplify the indicated limits on the following. 3x2+5 lim x-0 x²+1 + el-*] (i). (ii). lim…

A: 1) =?

Q: (fif2..f)is di fferentiable at x, proofthat ... by using f(x)– f(*.) f (x)=lim, x-x,

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Q: Using the definition of the derivative, find f'(x). Then find f'(-3), f'(0), and f'(4) when the…

A: f(x)=2x3+10

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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…

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Q: Computing the derivative of ƒ(x) = x2 ex

A: Consider the given function fx=x2ex

Q: 8r + 5tant Find lim t>0 sint

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Q: b. Determine if the lim f(x) exists, if f(x) is defined as follows: X4 12x + 3, 5x-9, x < 4 x 24…

A: Both question are solved as, follow

Q: Q.4: Prove or disprove, lim f(x) = 4 If f(x) = x # 2 x = 2' I-2

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Q: 1. Consider the function f(x, y) = 2y (a) Show that lim (x,y)(0,0) f(x, y) does not exist by using…

A: Note: if a limit exists at a point,it must be the same limit along any path approaching that point.…

Q: b) Suppose that limx→md(x) = 10 and lim,-mE(x) = -7 , find lim,-m(d(x) + E(x)) (iii) lim,-¬m(d(x).…

A: Since your question has multiple parts we will solve the first three parts for you. Consider that…

Q: Find the derivarlve find f2) uslv fla)= Linfatfay -a x-a Find derivative ECx)=3x"+| fiind f'(2)…

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Q: O3: A- Find the limit for the follo tan2x 1- lim x→0 sin4x

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

Q: please answer parts a, b, and c

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Q: Q3) Find the limits of the following functions V2+12-4 3.lim t2+t-2 tan3x lim X-0 sin8x 1. lím 2.…

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Q: -4x + 2 if r 2 Let f(r) = %3D -5x +4 if r > 2 Find lim f(x), if it exists. z+2 O DNE O-12 -6 0.

A: Given, fx=-4x+2 if x≤2-5x+4if x&gt;2 We have to find limx→2fx if it exists.

Q: For f(x)=√7x+2, find f′(x) using the definition f′(x)=limh→0f(x+h)−f(x)/h. f′(x)= Using this, find…

A: Equation of the line passing through the points x1,y1 and having slope m is y-y1 =mx-x1.

Q: 04: (chose one only) (3-x x2 a) Find lim, 2+ f(x), lim,-2-f(x) andf (2). b) Dose lim, 2 f(x) exist,…

A: 1. According to question,Given function,fx = 3-xx&lt;22x=2x2x&gt;2

Q: Q3) Using the definition, lim f(k+h)+f(k) h→0 ds calculate the derivatives dk of the function : S= k…

A: Using the definition of derivative have to find  dS/dk ,where S( k ) = k + 1/k.

Q: Q2 Find the limits of the following functions: 2-V-5 1. lim tan2r 2) lim -1 1-t-2 3) lim X0 tan4x 4)…

A: According to our guidelines we can answer only three sub-parts and rest can be reposted.

Q: nd the one-sided DNE lim_(x². +x+5) x--5- exists). (If an answer does not exist, enter DNE. Submit…

A: Topic:- limits

Q: tanx - x x-0 x - sinx 1. lim

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Q: Q2: (a) By using " L' Hopital rules "; Find the limits of ::- (1) lim,-(n/2)-(tan x)cosx (2) lim,--0…

A: L'Hôpital's rule states that for functions fx and gx which are differentiable on an open interval I…

Q: Using the Sandwich Theorem

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Q: tim Q2 Find the limits liw h +h cosh 1- Sinh.cosh 2-lim 2x-8

A: Limit value of the rational function

Q: Evaluate r3+3r2+3r+1 lim f. lim a. r--1 r+1 X+o x+1 e+x? 1-cos? 2x b. lim X-4 -3x+4x2 g. lim- 3x…

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Q: REFER TO THE GRAPH TO FIND EACH LIMIT, IF IT EXISTS.  Answer letter d, e, and f

A: According to given figure limx→0-fx=-1limx→0+fx=-1 We know that for any given functionfx at x=a if…

Q: M 27. (a) By graphing the function f(x) (cos 2x- cos x)/x %3D and zooming in toward the point where…

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Q: Given n ≥ 0;  explain that   limx→∞ fn(x)/(e^x) = 0.

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Q: Q3: A- Find the limit for the following functions: - tan2x 4х-3 3x3-9x2+x-3 1- lim x-0 sin4x 2- lim…

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Q: 3. If f and are continuous functions with f(3) 4 and lim 2f(x)-9(r)3D5, what is g(3)?

A: To evaluate the value of the function

Q: : A- Find the limit for the following functions: - tan2x 1- lim X-0 sintx 4x-3 2- lim x--0 Vx2+1 3-…

A: L'Hospital's rule states that for functions f and g which are differentiable in an open interval…

Q: -5x? + 2x for æ 0 According to the definition of derivative, to compute f'(0), we need to compute…

A:

Q: Q1) A) Find the tangent equation for the function: f(x) = Vx² + 5 at =2 ? B) Find the limits by…

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Q: O3: A- Find the limit for the following functions: - tan2x 4х-3 3x3-9x2+x-3 1- lim x→0 sin4x 2- lim…

A:

Q: – 4x + 8 if x 2 Find lim f(x) , if it exists. I2 O-5 O DNE 05

A: Function given is -        f(x)=-4x+8if x≤2-5x+5if x&gt;2 We need to find limx→2f(x) if ity exists.…

Q: 4f(x) + 2x – 14 Suppose that lim z+1 5. Find lim f(x). I→1

A:

Rate of Change

The relation between two quantities which displays how much greater one quantity is than another is called ratio.

Slope

The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as: