Express the limit as a definite integral. lim 3 Xk, where P is a partition of [2, 3] k=1.k

Q: 1. x² tan( + 47) + 2 tan-1x lim =? (a) 1 (b) -2 (c) -1 (d) (e)

A:

Q: Part. f. True or False: g(x) = In(x-1) is continuous for x > 1. 4 x +22

A:

Q: Find the limits of the Function 2 (x + h)² – x² lim h→0 h

A: We can solve this using the L'Hospital rule. And also from expanding equation we can solve easily.

Q: Find the limit. За + 5 lim x→0 x – 4 O -5/4 O DNE O 3

A: Limit problem

Q: Write the following limit as a definite integral: limn→∞ ½ / Σ²-1 ( ²1 )º n j=1 of th x6 dx f²x5 dx…

A:

Q: x² sin +y f : R² → R, ƒ (x, y) = %3D x + y

A:

Q: Find the one-sided limit V4 - y? lim y -2+ y + 2

A: Given: To find

Q: Int 17/(√₁i + -j+2t²k √ti+ 2 -. Evaluate the limit. lim lim

A: let  N=limt→1[ti+lntt2-1j+2t2k]

Q: III (20') Let X={1, 2, ..., 16} and define function f(x)=rx for all x € X where rx is the remainder…

A: Function f(x) = rx  where rx is the remainder when 3x is divided by 15. When x=1 We have rx the…

Q: 8. Express the limit as a definite integral and evaluate. 4i 7cos 3- lim i=1

A: Limits as a definite integral and evaluate

Q: Rn -5 +i n ||

A:

Q: Express the limit as a definite integral on the given interval. „m. 2 (3(x;)° – 6x;*]Ax, [2, 6] i =…

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.