Determine S, x² dx. Get Ax, x¡, and f(x¡) and sub. to lim E-1f(xi) · Ax. n→∞

Q: a) limn-o fn(x) for each r E [0, 1], and b) lim,- So fn(x) dx.

A:

Q: 3. EVALUATE AS AN INFINITE SEMES: 0.5 a. e dx lim x- In (1 + x) b.

A: We know that, ex=1+x1!+x22!+x33!+x44!+.........................=∑n=0∞xnn! and…

Q: Find lim F(t), where F(t) = (t² − 3)î+ e¹ĵ+ (sinët) k. t-∞ oîte²j Ⓒ 21 √zi+37 O None of the above

A:

Q: Find lim e" dt O 1/e 1

A: This is a special integral function, apply linearity and then solve.

Q: fr'e* for 1 <x<3' for 0<x<1 If (x)= {e then limf(x) is A. O В. 1 С. е D. e E. nonexistent

A: The given function is defined for the interval [0,1) and (1,3].

Q: Find lim eR dt x 00 1/e 1 e

A: We will find first integration then after we apply limit

Q: Which of the following is not true? A Sin(x²)dx= limin(x²)dx c (B) None of the given choices .5 dx ©…

A: Given:  A)∫0elnx2dx=limc→0+∫celnx2dx B) None of the given choices C) ∫05dx25-x2=limc→5-∫0cdx25-x2 D)…

Q: 2.r + y Find lim (x,y)→(0,0) 2.x²y + xy² or show that it does not exist.

A:

Q: Which of the following corresponds to the x-4 √x-2 evaluated? 0 4 2 DNE limx→4 ( when

A:

Q: Find lim (e* +x3/2+2x)/x. x+0+ e3/2 а. +00 Ob. Oc 1 d. e9/2 е.

A:

Q: Find lim e x2 dt X 00 0. ej

A:

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

A:

Q: Suppose if f(r) s g(x) < h(x) for all z€ (0, 2), what is lim h(x)? Select the correct response OA-1…

A: Solution: The objective is to determine the correct option for the given questions

Q: For f(x) = 3x*, find using the definition, dx dy Ay f(x + Ax) - f(x) lim Ax-0 Ax lim dx Ar-0 Ax (a)…

A: Given:- f(x) =3x4  To find:-  Using definition of derivative find dy/dx

Q: - Complete the following statement. (x? + 3) dx = lim where Ax = and x; is

A: To complete the statement

Q: For n > 0, use Taylor's theorem to find (1+x)!/n – 1 lim 3.

A: Explanation of the answer is as follows

Q: Which of the following is not true? (A) None of the given choices 3 dx dx Ⓒ = S B S³ = In(x²) lim c→…

A: An integral assigns numbers to functions in a way that describes displacement, area, volume, and…

Q: -2x 39. lim (e* cos x)

A:

Q: (1) For each of the following, find the I (a) lim(z,y)→(0,0) V=²+y² zyd (b) lim(z,v)→(0,0) 2r² +y* ·

A:

Q: |8x – 1|+ 2 (b) lim T→士o 7 – 4.x Hint: you will have to consider the limits at oo and at —00…

A: To calculate: limx→±∞ 8x-1+27-4x   Now, limx→∞ 8x-1+27-4x 8x-1 is positive when x→∞.  Therefore…

Q: ах? + bху + су? y-0 dx + exy + fyx“ ax? + bxy + cy 2. Evaluate lim lim- – lim lim y-0 x0 dx +exy +…

A:

Q: Find the limit. 3 - ti + In(t)j k t-3

A:

Q: lim, „(Væ² + x – x)=? O a. 0 O b. 1 O c. Limit does not exist O d. 00 O e. 1/2

A: In these type of questions just rationalize the given term and simplify the fraction before finding…

Q: e* – 4 , x< 3 - Let f(x) =- cos(x) %3D x2 3 lim f(x) = x 3 O DNE e3 – 4 - O 3 O cos (3)

A: Here we have to find the limit value.

Q: t t→0 et (c) lim = 1 True False

A:

Q: be an antiderivative of X e *. Find lim F of these

A: We have to choose the correct answer from the given options according to the given information

Q: Determine the value of c for which 42 8n lim (1+ n00 cn

A:

Q: Sirlw)dk= f (x) κ= lim Σ fx%) Δx 25.) Use the definition, -2x n+00 i=1 to evaluate Σ Ei=" (n+1) Eř="…

A:

Q: Given that J(9, -4), K(6, -10), L(1, -1), and M(x, 4), find the value of x so that JK LIM.

A:

Q: Show that for any e > 0 and S, 1X₁, lim P(|S₁-81 ≥ 2) = 0. y'a 3140

A: We will use Chebychev's inequality to find the required limit of probability.

Q: for |x| > 1, 2x2 fx,(x) = 0, %3D otherwise. Let L = lim P(max{X1,..., X,} < n log(v5)). Determine…

A: Let Xn be a sequence of random variables such that,

Q: [VALUATE THE LIMIT OF THE GIVEN FUNCTIONS: 3 x→1 TT-X² 2

A:

Q: e n Show that for any &> 0 and S, ₁X₁, lim P(S₁-0 ≥ 8) = 0. =

A: We will use Chebychev's inequality to find the required limit of probability.

Q: How can I find A, k, and C with the following information? L(t)=-(A/k)e^(-kt)+c Lim as t approaches…

A: Given function,

Q: Which of the following is not correct? 4dx 4dx A Jo Jx(x+6) = lim o Vx(x+6) C+ .3 dx .3 dx B h…

A:

Q: dy For f(x) = , find dx using the definition, 19x dy f (x + Δx)- f(x) Ay = lim Ax-0 Ax = lim dx Ax→0…

A: The derivative represents the rate of change of a variable y with respect to x. This implies for…

Q: Using the Sandwich Theorem

A:

Q: 1(a)Find y' given that y In(2x + 1) + e**+5 %3D 5x2-1 b) Evaluate lim x00 2x2+1 c) Find y' if x'+ y…

A:

Q: lim e 0 t/ Select one True False

A: limx→0+e1xusing chain rulelet f(x) =1xg(u) =eulimx→0+ f(x) = limx→0+ 1x =∞

Q: 13. ebx cos x dx exists only when b < 0. lim t→∞

A:

Q: II. f(t) = cos t, lim h

A:

Q: Evaluate the limit *dx – x – 4aª lim 3 A) В) 1 C) D) 4 E)

A:

Q: 'e in + = "T 2n Find lim a

A:

Q: g lim y²+6y y¬T [/y+1-3y2 y+1-3y²

A: Using standard limit substitution

Q: Ex let yct) soluton to the I.V.P y"-y'-2oy=0, yco) =3 , yto) = b If . Lim yL)= O find b?

A: Explanation of the answer is as follows

Q: D Find lim X,Y)→ (5,1) XY X+y or show it DNE.

A: We have to find limit

Q: Which of the following is not true? Ⓒ √ 4dx √x(x+6) c lim dx ⒸS₁² 25² + x² ² m 25-x2 B dx c-5-0…

A:

Q: Find lim e dt 0. 1 1/e

A: We find out limit of given function. See 2nd step.