Q: d. State the equation of the vertical asymptote of f(x)=log, (x+1). e. Sketch a graph of f(x) = log,…
A: We have to find the asymptote of function and graph
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A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…
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Q: lim (-5) (²²-4x-5) x-5,
A: NOTE: Refresh your page if you can't see any equations. . first, we need to find the factored form…
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A: We have to evaluate the integrals.
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A: The objective is to find the general antiderivative.
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A: The given problem is solved below in detail.
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A: We can answer all the three questions as below.
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A: I am attaching image so that you understand each and every step.
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A: topic- vectors
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A: x-2y+5=02y=x+5y=x+52The equations are: y=x+52y=e2x
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Q: 3.) Find the directional derivate of f(x, y) = tan¹ (3xy) at the point (1,2) in the direction of…
A: We have to find directional derivative
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A: As per Bartleby guidelines for more than one question asked only one is to be answered please upload…
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Q: 2. Evaluate the limit assuming that lim f(x) = 3 and g(x) = 1. x--4 (a) lim f(x)g(x) x-4 (b) lim…
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Q: 1 B) Find all of the second derivatives for f(x, y) = (3xy² + 2xy + x²) In; x²+y²
A: To find all the second derivatives for fx, y=3xy2+2xy+x2 ln1x2+y2.
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A: To find out the components of vector v.
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Q: Find the divergence of the following vector field: 00 O 2z O F = (y, -x + z², 3x)
A: We can solve this as follows:
Q: 1. If f(x) = cos²x, then the derivative, f'(x) = ? a) 2sinx b) −2 sin x cosx c) 2cosx d) 2 cosx =…
A: We are authorized to answer one question at a time, since you have not mentioned which question you…
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- Suppose that we observe that X1, X2, . . . , Xn are iid∼ U(0, 1). Show that X(1)converges in probability to zero.Prove the conditional convergence ofR = 1 +1/2 +1/3 − 3/4 +1/5 +1/6 +1/7 − 3/8 +···Use the Cauchy Condensation test to prove that ∑ n = 2 to ∞ 1/( n (ln(n))^ p)) converges if p > 1 and diverges if p ≤ 1. (Make sure you verify that the hypothesis of the Cauchy Condensation test are met)
- Find the interval of convergence of ∞∑n=0 ((-1)n (x+1)n )/ (2n).Let fn(x) = nx/1 + nx2 (d) Is the convergence uniform on (1,∞)?. Let gn = nχ[1/n,2/n] and g = 0. Show thatZ 20g 6= limn→∞ Z 20gn.Does the sequence (gn) converge uniformly to g? Does the Monotone Convergence Theoremapply? Does Fatou’s Lemma apply?
- If a power series ∞ n=0 anxn converges absolutely at a pointx0, then it converges uniformly on the closed interval [−c, c], where c = |x0|.Provide a proof using the monontone convergence therom that x_n convergesSuppose the sequence {an}∞n = 0 is defined by the recurrencerelation an + 1 = (1)/(3)an + 6; a0 = 3.a. Prove that the sequence is increasing and bounded.b. Explain why {an}∞n = 0 converges and find the limit.
- a) Suppose (an) is Cauchy and that for every k ∈ N, the interval (−1/k, 1/k) contains at least one term of (an). Can we say that (an) converges to 0? Either show that it does or give a counter-example.does this geometric seris converge to... 4/5 4/3 2/5 2/3Prove that the sequence {cn} converges to c if and only if the sequence {cn- c} converges to 0.