Q:Discuss the continuity of the function f(x) =lim+ sinTt x)" - 1 n- (1+ sinTt x)" +1 at the point x = 1.

Q: Find the limits x2/3 + x1 lim X00 x2/3 + cos?x

A: Given: The function is f(x)=x2/3+x-1x2/3+cos2x   To determine: limx→∞ x2/3+x-1x2/3+cos2x

Q: Use the graphs of f and g and their tangent lines at (2, 0) to find lim x) x-2 g(x) y = 1.4(x – 2) y…

A: NOTE: Refresh your page if you can't see any equations. . for the graph f, the equation of the…

Q: 1- Evaluate the limit a-Lim(x/(x-1)-1/ Inx) x-1+ d- lim x+1/√2x²+x+1 x-→∞ b- lim [In(cos(x))]…

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Q: 35. Use the Squeeze Theorem to show that lim,-o (x² cos 20TTX) = 0. Illustrate by graphing the…

A: To show that: limx→0x2cos20πx=0 Using Squeeze Theorem:…

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

Q: 35. Use the Squeeze Theorem to evaluate lim f (x) given that on the interval (2,3.5) 15 Inx - 3x²…

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Q: Find Lim as x approaches 0 of the function cos(4x-1)/2x

A: Given: limx→0cos4x-12x To find:  The limit limx→0cos4x-12x

Q: tan 3h 3. Estimate the value of lim,0- by creating a table of function values for h h = 0.01,0.001,…

A: We need to substitute these values of h in function f(h) to evaluate limit

Q: Find the limit. cos(x) – 1 +x2 lim x-0 2x4

A: It is given that, limx→0cosx-1+12x22x4.

Q: Find the limit. lim (1+ sin(3x))/* x→0+

A: Given: u=(1+sin(3x))1x We want to find  limx→0+u=limx→0+(1+sin(3x))1x Since we know that u=eln(u)…

Q: Let f (x)=x²-2x + . Find the slope of the graph y = f(x), at point P- (0,7) evaluating th'e limit AX…

A: fx=x2-2x+1 We need to find the slope of the graph at the point P0, 1

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: Q1: Find the Limits of: Тan x 1- lim X+Sin x+VX 2- lim xo X+Sin x 3- lim vx2 + 1- Vx2-x

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Q: Convert the limit to the indeterminate form 0/0 and then evaluate the limit. lim(x-1)tan(pi(x)/2)…

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Q: lim (sin?x x-0 x2

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

Q: Find the limits lim x→ -1+ cos-1x

A: We find the limit by substitution

Q: is lim x = inf (xn) as x, y. What Express answer and = 3n lim sup (xn) where Xn = [(-1)³ ]+2?

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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)…

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Q: find the limit as x approaches infinity of (1+2/x)^x

A: Find the limit as x to infinity,

Q: Use the Squeeze Theorem to show that lim (x2 sin(2)) = 0 x-0 %3D

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Q: Suppose f(x,y) = sin-' (6 – 2x2 – y²) and g(x,y) = 4x2 – y2. Determine the continuity of the…

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Q: If lim | f(x)dx does not exist, b00 a then | f(x)dx diverges. a Select one: False True

A: True  Improper integral said to be convergent if the limit is finite and that limit is the value of…

Q: Evaluate the limit of a. 3 b. O tan 2x-2sinx as x approaches to 0. c. Undefined d. Infinity

A: As per our guidelines we are supposed to answer only one question. Kindly re-post other question as…

Q: Now consider the equation for the function above: ex+2 + 4, Vx + 3 + 1, х 2 f(x) 2, 3x, Use the…

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Q: Let fn(x) = n²x²(1 – x) on [0, 1]. Does lim,-00 So fn(x) exist?

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Q: )Use the Sandwich Theorem to show that lim cos x-1 =0. x2 Find f'(x) for f(x) = sec(vx2 + 1).

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Q: - Define the function f:R → R by ƒ (x) = x +1 if x 0 and f (0) = 4. Show that lim,-0 f (x) = 1 and f…

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Q: (1point Use continuity to evaluate lim sin(-8x + sin 5x) Enter I for oo, -I for -co, and DNE if the…

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Q: The following limit represents the derivative of a functionf at a point a. 5 tan 6. V3 f '(a) = =…

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Q: f'(0) = Is f(1.5)>0? ('Yes on not) lim fCh-)-f(-)

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Q: Prove rigorously that lim sin 1/x does not exist.                                    x → 0

A: Let the given limit be y - y = limx→0 sin1xy = limx→0 sin1x1x×1xy = limx→0 sin1x1x×limx→0 1xy =…

Q: Determine the limit as x approaches the given x-coordinate and the continuity of the function at…

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Q: Find the limit of tan^-1(e^(x^2)+x^2+1/x) as x approaches negative infinity

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Q: 4. a) Explain using theorems from Section 2.5 why the function is continuous at every number in its…

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Q: Evaluate using the Squeeze Theorem.

A: Given: limx→0 x sin 1x2  To evaluate: The limit using Squeeze theorem.

Q: Find lim 2x sin using the Squeeze theorem. x-0

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Q: Use continuity to evaluate lim sin(2x + sin 3x) Enter I for o, -I for –o, and DNE if the limit does…

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Q: a)Express the limit as a definite integral. Σ (3c-5)Ax, xe[0,1] lim 2 b) and then evaluate it.

A: lim∆→0∑i=1n3c2i-5∆xi  x∈[0,1]∑ =∫∆xi=dx∫01(3x2-5)dxThis is definite integral

Q: ). Determine the interval(s) on which f(x) =4x−12x−1is continuous. b). Find lim x→0…

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Q: Find the limit: 1 – cos(x) lim x2

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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: Find the limit as x approaches zero of f(x)=tan(x)/x

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Q: Let fn → f, where if 0 <x < L3 (3 – x) if 1 < x<1 { fn (x) п-3 if 0 < x < 1 - and f(x) if x = 0 Then…

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Q: 2) Use the definition of the derivative f(x+h)-f(x) lim hー→0 to find the derivative of f(x) =…

A: Our objective is to find the derivative using definition.

Q: Evaluate T COs(T-a)-sin 글(ㅠ- z) - ㅠ lim T - x

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Q: 4. a) Explain using theorems from Section 2.5 why the function is continuous at every number in its…

A: We have to solve given questions.

Q: Use the limit definition to find the derivative of f(x) = 5x? + 2x – 7 at x = -2. Show all 1. :…

A: Consider the provided function, fx=5x2+2x-7, x=-2 find the derivative by using the limit definition.…

Q: Now consider the equation for the function above: 2x + 3, x 4 - x-3 ’ 2, x = 4 Use the equation and…

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Q: Prove that lim n 00 a" f (x) dx = 0, for any f E R[0, 1].

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Q: Compute the lim as x goes to 0+ (e^x - 1 - x)/ (xe^x - x)

A: we have to compute the limx→0+ex-1-xxex-x