1. Use the limit definition to evaluate ,(2 – 3x)dx.

Q: Evaluate the following by limit of su (3x² +5)åx (sin x)dx

A: Solution:To find the integration Formula:∫xndx=xn+1n+1+Csin2x=1-cos 2x2∫cos ax=sin axa+C

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

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

Q: Determine the following limits analytically.

A: Given: L=limx→-1x2+8-5-4xx3+1 For evaluating given limit, we substitute x=-1+h, h→0 So,…

Q: In Exercises 7 through 12, find dy/dx using the limit definition. 7. y = -2x' +x - 3 8. y = 3x - 4x…

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Q: Tim (X-1)sec(Tix/z) X -

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Q: Use the figure to find the limit a in the interval [a, 4] such that f (x) dx is smallest. f(x) + 2 3…

A: To solve the following problem

Q: Calculate the following limit: lim(4z)* sin(). エ Y0 Türkçe: lim(4r) sin() limitini hesaplayınız. エY0

A: To evaluate the given limit

Q: Is the limit of f (x) as x approaches c always equal to f (c)? Why or why not?

A: To prove :                   The limit of f(x) as x approaches c always equal to f(c). Answer :…

Q: x³ + x²y+ 2y³ x² + y? ,3 lim (x,y)→(0;0)

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Q: Find the limit (if it exists).

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Q: 2.a²y rª + y? Show the function f(x,y) : has no limit as (x, y) → (0,0)

A: We have to show that the function fx,y=2x2yx4+y2 has no limit as x,y→0,0.

Q: By computing the limit of right-endpoint approximations, prove that b4 x' dx 4 if b > 0, then

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

Q: Find the limit. Jlim ( arctan(4t), e-7t, In(t) е tco

A: Given information:

Q: O The limit function of h. )= n'Sinx i+n?x is?

A:

Q: find the limit lim l-cos(t, ス→ dx

A: Given: limx→01-cos xx2 To Find: Value of given limit

Q: 8. Evaluate the limit dx lim C) E) 3 B) 1 D) 4

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Q: 2) Use the definition of the definite integral to write 2 e* dx as a limit. Do not evaluate this…

A: In this we use the limit  definition of definite integral

Q: Evaluate the following limit. sin xy + cos xy 2y lim (x,y) →(0,)

A: The objective is to evaluate the limit.

Q: Find the following limit. x2 + 16 lim (x, y) → (0, 18) arctan x² + (y – 18)2,

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Q: 4x-1 dx using right endpoints x = a+kAx.

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Q: Find the limit for the following sin(3y).cot (5y) lim y→0 y.cot (4y)

A: we have to find the limit of the following.

Q: Rewrite , 15 dx as a limit and then show that the integral diverges.

A: Given

Q: lim, (5 イータ 1-Sint Cos C)

A:

Q: Is it true or false: that a two sided limit of f(x) as x approches c exist if the value of f(c) does…

A: The statement is given as a two sided limit of f (x) as x approaches c exist if the value of f (c)…

Q: Calculate the following limits, if they exist. lim (7,y)→(0,0) 1 – cos(x² + y²) 1² + y²

A: Use the polar coordinate substitution

Q: Find the value of the following limits: 5y 1-limy→0 tan 10y

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Q: What is the limit of (e^x-e^-x)/( sin (x)) as x approaches 0?

A: we have find the value of limx→0ex-e-xsin x

Q: What is the limit of f (x) = 1 as x → T?

A: Value of a constant function is always same irrespective of input.

Q: Evaluate | re dx by changing from x-limits to u-limits. xet

A: Explanation of the solution is given below...

Q: Apply the two path test to make sure the following limit exist or not at (0,0) ry f(x, y) x³ + y3/2

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Q: Find the limits in Exercis

A: To find the limit of limθ→01-cos θsin 2θ, substitute θ with 0 and the indeterminate form of limits,…

Q: What is the limit of g(t) = t as t → π?

A: We find the limit by substitution

Q: What is the limit of (In(e+h)-1)/ h at h=0?

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Q: Let f(x, y) = 2*. Find fy(1, 2) using the limit definition.

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Q: Evaluate the limit using L'Hospital's rule e – 1 lim I+0 sin(2x)

A: The given limit is in 0/0 form.

Q: compute dy/dx using the limit definition.

A: Plug the given equation in the limit definition

Q: . Apply the two path test to make sure the following limit exist or not at (0,0) xy f(x, y) x³ +…

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Q: Find the limit, if it exists, or type DNE if it does not exist. eV(1z²+1y²) _ lim А. (x,y)→(1,–2)…

A: Given the limits function

Q: Use the definition of the integral to write sec x dx as a limit. Do not evaluate the limit.

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Q: O The limit function of h. )= n'Sinx is ?

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Q: What is the limit of f(x) = 5 as x approaches a? (If an answer does not exist, enter DNE.) dne Need…

A: Solve simply

Q: Use the limit definition to compute f '(a) and find an equation of the tangent line. f (x) = x−1, a…

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Q: Find the limit. lim ey sin P -(5, 0, -5) O 1

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Q: What is the the value of the limit lim,o Vn (Vn +1– yn)?

A: Limit of the sequence

Q: Let sin(2t) F(t) = + cos t, Find the limit lim F(t).

A: We have to find the limit

Q: Apply the two path test to make sure the following limit exist or not at (0,0) ry f(x, y) = x³ +…

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

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Q: Evaluate | e* dx as limit of sums. a

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Q: compute dy/dx using the limit definition. y = 4 − x2

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Q: if r =-1 A if z + -1 2. Is f(r) = continuous at r =-1? (Show your work using limits.)

A: