Find the equation of the tangent to the curve y = 2x² – 1 at the point where z =1. Use the limit definition to find the slope.

Q: Explain how the Limit Comparison Test works.

A: Let ∑ak and ∑bk be two positive term series, and limk→∞akbk=L. 1. If 0<L<∞(i.e. L is a finite…

Q: Evaluate the limit.

A:

Q: 1- r + In (x) lim 41 1+ cos (3a x)

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Q: Evaluate the limit.

A: We divide the numerator and the denominator by x

Q: Can anyone please explain what limits are? And why limits are used?

A: The detailed explanation of limits is  given below in next step

Q: Evaluate the limit.

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Q: Evaluate the limit.

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

Q: fim 1 t->-∞ 1 + cot = "= 8

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Q: Evaluate the limit.

A: Consider the following limit: limx→∞3x2+20x2x4+3x3-29 Divide numerator and denominator by x4:…

Q: Please evaluate the limit.

A: Given,

Q: 10x2 + 11xy + lim --1,10) 10х2 — 39ху -

A:

Q: [(x³+1)] lim X→-1 L x+1

A: To find limx→-1x3+1x+1 We know that  a3+b3=a+ba2-ab+b2 Let a=x, b=1…

Q: cos((x) – sin(x) – 1 х) — 1 - 5. lim x→0 2.x

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Q: xy + yz + xZ lim (x,y,z)→(0,0,0) x² + y2 + z²

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Q: -12 –10 -8 -6 24 6. 12 8. en + n 6

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Q: limx→→∞ √1-x+2x+7 2 9x +5 - 3x

A: limit.

Q: Let f be a continuous function from R to R. Prove that { : f(x) = 0} is a closed subset of R.…

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Q: evaluate the limit.

A:

Q: -3x3 Evaluate lim Зд3 — 42 + х — – 10 - -

A: (1).    We have to find the limit: limx→∞ -3x33x3-4x2+x-10

Q: Evaluate the limit.

A: To evaluate the limit: limx→-∞3x3-10x+4. Solution: Evaluating the limit.…

Q: evaluate the limit.

A: Given integral is When x=0 Therefore, by applying L'Hopitals' Rule, we have