Find lim r(t) when 5 In t r(t) = (: 2 tan¬lt, e-2 t 2 tan-t, e 1. limit = (2т, —2, 0)

Q: e) sec mx – 1 lim

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Q: If f(a) - (9x 3), then lim f(x) = エ

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Q: Find the limits

A: Given: Function  To Find: Limit of the function at the given point

Q: a) Write down the definition of the derivative in terms of limits. Using this definition find (x² –…

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Q: 2. Let f(x) be a continuous function on R. The following is known about f(x): • The domain of f(x)…

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Q: limx, y→0, 0 3 sin(x) sin(y) ³ cos(x² - ₁² 1- cos L

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Q: 6. Let r(t) = <-X²₂00- (a) Find lim r(t). k→0 (b) Find all values t and k for which r(t) is not…

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Q: Q2. Show limit DNE зеуг 101n(x) lim (x,y) → (0,10)

A: Q2 asked and answered.

Q: 3. Find the limits for the following functions by using L'Hopital's rule: 1- lim 1- sin x 1+ cos 2x…

A: Thank you

Q: Sin@t) Sin (2+) In (tan (2€)) In Con (8t)) Let F(t)= (t + 1) Cos (3€) Find the limit F(t) tso

A: Given,           Ft=sin3tsin2ti+lntan2tlnsin3tj+t+1cos3tk

Q: (d) Determine the following limit using u-substitution method: sin(t - 1) lim -1t2 +t – 2

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Q: 1) limy-o 2ytan(1/y) sin(r-0²) 2) lim2n 101-Va 2 3) limg-n/2 (n²-482 )sec\ß] tan2x 4) lim T

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Q: 1.(2.2) Find the limit. (1) lim 5x x-0 sin 4x (2) lim 2x3+3y4 (x,y)(0,0) x2 + y² 2.(2.3) Let f(x, y)…

A: Since you have posted multiple questions, we will provide the solution only to the first question as…

Q: 1-cos r-r² 1) lim,-0

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

Q: Sketch the graph of a function f that has all of the following properties: (i) (ii) (iii) (iv) f(1)…

A: Given (i) f(x)=f(-x) The curve should be symmetric with respect to y-axis. options (3), (4), (5) and…

Q: 2. Evaluate the following limits if they exist: sin(x2 + y?) (a) lim (x,y) (0,0) 2x² + 2y2 xy (b)…

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Q: Find lim,9)→(5,-1) (x³ + 4.x°y – 2xy²) . | 1. 3615 2. 3635 3. 2635 4. 2615 5. 2605

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Q: II. Evaluate the limits. tan 0 2. lim 0 -0 sin 20 (y-#)* 2. 4. lim t 1-sin y y - 2 2.

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Q: Find the limit, if it exists. Be sure you can explain your answer. lim (9r (1,4) >(0,0) - 8y? + 6e²²…

A: The given expression is: limx,y→0,09x2-8y2+6ex2-y2,cos8xy

Q: Find the value of the limit lim sin 6 t t - 0 sin 4 t (a) 2 (b) 1.5 (c) 1.7 (d) 1.9 (e) 1.8

A: Recall the famous rule of limit:

Q: 1. lim n2+5".

A: As per our guidelines we are supposed to answer only one question. Kindly repost others question as…

Q: cos x b) Evaluate the limits: (i) lim x→ 0 \2x 4 1 (ii) lim[ x- 2'x2-4 х-2-

A: The objective is to evaluate the limit.

Q: 3. Let f(x) = x and P = {0, nn = 1}. ... + f("1) and that lim Lf(P) + k = k(k +1)/2) 1 Show that…

A: Given the function f(x) = x &amp; a partition of the interval 0,1 as P =0,1n,2n,3n,...nn=1. First we…

Q: r(t) = YouTrylt 1 Find the domain of: /sint r(t): YouTrylt 2 Let limr(t) . Find the limit: -

A: We have to find the 1) Domain of r(t)=1t,t,t2 2) let r(t)=sintt,t,cost find limt→0r(t)

Q: Find lim (x,y) → (0,0) 4e4y sin (2x) X 4e4y sin (2x) X lim (x,y) →(0,0) (Type an exact answer.) =

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Q: Find the lim ex-y limit or (xy)-> (0,1) 2 cosx-1-y Show that it does not exist. DNES

A: To find the limit .To show that it does not exist.