Let - .12 Let /= -dx. Select all that apply , x³-343 Your answer: O The integral is improper of Type I. 49 - 49 343 12 343x 12 3 .12 3 3 dx D x3 – 343 x² + 7x + 49 X-7 O The integral is convergent. 49 49 + 14 112 arctan 3/3 t-7 112 arctan 3/3 38 |= lim In 1+7+ 3 277 |t²+7t + 49 7/3 7/3 49 95 + In 277 49 arctan V3 31 | = 7/3 49 (2t +7 7/3 t-7 49 -arctan V3 3 - lim In 1+7+ (Vt?+7t + 49 O The integral is improper of Type II. O The improper integral is divergent.

Q: La e* dx 3-2e*

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Evaluate n lim > sin n i=1

A: Given

Q: The graph of g(u) = -4 -1 -3 -3 + (-2u + 2)du = -2 - Q Use the limit definition of the definite…

A:

Q: Evaluate the definite integral by the limit definition

A: Here,

Q: Consider the sequence of functions {Sn}n=2 where fn: [a, b] → R defined for n 2 2 by if 0 sxs -n°…

A: Given the sequence of functions as .Let us find the limit of the function  in interval [0,1].As n→∞,…

Q: Write the following expression in algebraic form: sin(arccos (6x)) V1-36z2 O VI – 36x² O VI – 6x² O…

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: lim x2 Vx2 e) lim xe? In2 x-5 ln a+6 In x-2 Ps

A:

Q: Evaluate using the Squeeze Theorem

A: To find the limit  limt→0+sinttan-1lnt

Q: A definite integral Evaluate In x dx.

A:

Q: The graph of h(x) = - -6 -5 -4 -3 3 15³ ( - 12/3 -x + 9 2) a 4 Use the limit definition of the…

A:

Q: Use the definition of the integral n | f(x)dx = lim f(x;)Ax a i=1 (where Ax = (b – a)/n and x; = a +…

A:

Q: Q.3 Find the value of x, for which the geometric n series Σ(3) (x + 4)" converges.

A: Note:As per our guidelines we are supposed to answer only one question if there are multiple subpart…

Q: lim as x approches 0 of cos(6theta)-1/sin(7theta)

A: Given: fθ=limθ→0cos6θ-1sin7θ Apply limit by substituting θ=0 in the above expression.…

Q: 5. 0 sin² x x² + 1 xp

A:

Q: Write the limit as a double integral and evaluate the definite integral. limm- ΣLa(15 +4#)을 Σ1154 n²…

A:

Q: o lim x-0 x² - sin²2x 2 x 2

A:

Q: -e lim te Int - 1

A:

Q: Evaluate 2. S sec*x tan*xdx

A:

Q: 2 E2 72-00 (i = 1 Express lim + Si ⅱ) (2) as a definate integral.

A:

Q: Show that f is continuous on (-0,00) sin x if x 4 V

A:

Q: Use the limit definition to evaluate the integral. Do not use the Fundamental Theorem of Calculus!…

A:

Q: "INT" function (alternative name is "Floor" function) returns integer value closest to the Input…

A: INT function or floor function of x is the greatest integer less than or equal to x.

Q: Using right end points, express the integral below as a limit using the definition of a definite…

A: The definite integral ∫-48x2-4x+x3dx Using right end points, we have to express the integral as a…

Q: 7- sin-(e*) 2 lim V1 - e2x

A:

Q: (x-sin x) A- Find lim,-0 1-cos X/

A:

Q: Express the limit lim,, +00 Ei-1 8i2 as a definite integral.

A:

Riemann Sum

Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence this method makes it simple. Usually, we take the help of different integration methods for this purpose. This is one of the major parts of integral calculus. 

Riemann Integral

Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.