Q1/ Find the equation of a line passing throug line passing through (2, –3), (5, –4). Q2/ Find the limit of the following function: 3x2-x 1. limx→0 2x2+7x 2+3x 2. limx-0 7x² -5° Q3 / Find a so that the function f(x) is contin x? + aх, x < 2 Where f(x) (sin-2x, x> 2

Q: (2x – x? if 0 sxS2 if 0 sxs2 2 -x if 2 < x<3 x - 2 if 3 <x < 4 if x 24 f(x) =

A: We have to find

Q: Q2) find the value of each limit sint 1) lim(- 1+cost +tcost C+cost x+xcosx 2) lim 0 sinxcosx

A: The limits of given functions are given as follows :

Q: Let (7z 2x2 for I<0, 8z2 + 7x for r20. f(1) = According to the definition of the derivative, to…

A: Given : Derivative any function is as follows let   f(x)= xm

Q: Find the limit lim Vz +1 Enter I for o0, -I for-oo, and DNE if the limit does not exist. Answer

A:

Q: Find the limit for the following functi * - y + 2Vx - 2Vy Vx - Vy lim (x, y)(0,0)

A: solve the limit

Q: For the function given by q (x)= x² + 2x+1, use the limit definition of the derivative to compute…

A: Definition of the Derivative:        The derivative of f(x)  with respect to x is the function f'(x)…

Q: Find a value for the constant "a" that will make the function f(x) continuous. f(x) = { ax- if xs2…

A:

Q: Use the limit definition of the derivative function to find 4 x2|. Which of the following is the…

A: We need to evaluate the correct step that comes just before using the direct substitution to…

Q: O:: A- Find the limit for the following functions: - tan2x 4x-3 3x3-9x²+x-3 1- lim x→0 sin4x 2- lim…

A: A) Note: We’ll answer the first question since the exact one wasn’t specified. Please submit a new…

Q: c) = = 4x + 1. If the limit does not exist enter DNE. ] lim h→0 ƒ(6 + h) − ƒ(6) h

A: Topic:- calculus

Q: Q2: (a) By using " L' Hopital rules "; Find the limits of ::- (1) lim,-(7/2)-(tan x)" (2) limy-o…

A:

Q: Evaluate the limit 3(y²1) lim y 4 7y²(y-1)³

A:

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

A:

Q: s*(2t-2)² dt (a) Find the limit (if exist): lim x 2х-1

A: Result 1 : If limx→af(x)g(x) = 00 , then by L hospital's rule limx→af(x)g(x)= limx→af'(x)g'(x)…

Q: Compute the limit 1 a2 1 - x2 lim xa x а - What can you say about the derivative of f(x) = ?

A: Given limit :

Q: Q3: A- Find the limit for the following functions: - tan2x 4х-3 Зx3-9х2 +х-3 1- lim x→0 sin4x 2- lim…

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

Q: Find the limit limit x tends to (1/2) 4x(3x+4)2

A:

Q: find the slope of a curve y = x2-2x-2 at the point P(3,1) by finding the limit of the secant slopes…

A: Given yx=x2-2x-2           P3,1

Q: if f(z) = V3+ 3z, find f'(3), using the definition of derivative f'(3) is the limit as z+ of the…

A: Given query is to find the derivative using definition.

Q: Find the value of b-2a for which the limit ex – xex – cosbx - limx +0 exists 4 Select one: а. 3 b. 1…

A: L'Hospital's rule is a useful method to find the limits of indeterminate form. There are two…

Q: Evaluate f(4+ h) – f(4) lim h0 where f(x) =5x +7. If the limit does not exist enter DNE. Limit =

A: f(x)=5x+7

Q: Find the limit of xsinx as x approaches 0

A: Given:

Q: Q3) Find the limits of the following functions V2+12-4 3.lim t2+t-2 tan3x lim X-0 sin8x 1. lím 2.…

A:

Q: Show that the limit of the function does not exist xy lim (xy)-(0,0) x2 + y?

A: We have to show that limit of the function does not exist.

Q: Find the limit, if it exists. x² ycosx x* + y² lim(x,y)¬(0,0)

A:

Q: Find the value of the.limit Olim Jx+z - V3 X+2 @lim Vx+6 x3-2 X+2

A: A number M is said to be the limit of a function f(x) at x=a if for any arbitrary chosen positive…

Q: Find the limit of the function along the x-axis xy lim (x.y)-(0,0) x2 + y?

A:

Q: Find the limit: 4z4 – 4y4 lim (1,9) → (3,3) 4yª z² - y?

A: lim(x, y)→(3, 3) 4x4-4y4x2-y2

Q: Find the limits of the functions below a) limr-3 x* sin x b) lim,

A:

Q: Find the limit. lim (x,y) → (1,−4) 3x²y 2 1+xy²

A: I am attaching image so that you understand each and every step.

Q: Let fa)=S(-5-x2 + 23x +19 f Xチー6 if X= -6 calculate the following limits. ENter DNE if the liniit…

A: l

Q: f(8+ h)-f(8) lim h-0 where f(x) = 2x + 5. If the limit does not exist enter DNE. Limit =

A:

Q: Find the limit, if it exists. (If an answer does not exist, enter DNE.) lim x²yeY (x, y) → (0, 0) x4…

A:

Q: Find the limit if it exists, or show that it does not exist. lim (7,v)>(0,0) xª + 4y²

A: According to the given information, it is required to find the limit of the given function.

Q: Q8:- Find the limit of the following functions:- x2 - 2xy + y (1) Lim (х,у) —>(0,0) X+y ху — у — 2х…

A: First we simply numerator by applying appropriate identities or factorization of it

Q: S -2x? + 5x 7x² – 5 for x 0. According to the alternate form of the definition of the derivative,…

A: Given:

Q: Evaluate the limit V9n4 + 13n³ – 5n – 10 lim -V25n16 + 5n² – 9n Also, find the asymptotic value of…

A:

Q: Q5. Evaluate the limit Vx+h- Vx lim h-0 Vx+h+Vx in the two cases (i) x > 0 and (ii) x = 0.

A: Evaluating:                                    limh→0x+h-xx+h+x   In the cases:…

Q: : A- Find the limit for the following functions: - tan2x 1- lim X-0 sintx 4x-3 2- lim x--0 Vx2+1 3-…

A: L'Hospital's rule states that for functions f and g which are differentiable in an open interval…

Q: Find the limit by numerically. 1 lim 1 + |t| |t – 1| t-0

A: To find the limit numerically, consider approximately some values of t which are closer to 0 from…

Q: Use the limit definition of the derivative f (x) – f(a) f'(a) = lim - a to find f'(a) in each case.…

A: Given fx=x3-7

Q: Find the limit: -3t e to - 1 t10 – t9' 2+ t -5 lim( t t→0

A:

Q: Q3) If the function {2x +1 lx² + 2 x> h) x <hS f(x) = having limit at x = h. Find the value of h.

A:

Q: Estimate the limit numerically if it exists. (If an answer does not exist, enter DNE.) lim x→+∞…

A:

Q: Find the limit (if it exists). (If an answer does not exist, enter DNE.) Sx2 - 4x + 6, X < 3 lim…

A:

Q: Find the limit: lim (1,y) → (0,0) x² + 8y?

A:

Q: Find the limit of the function along the path y = 2x X-1 lim (x.y)-(0,0) y -1

A: We have to find the limit of the function along the path

Q: Q8:- Find the limit of the following functions:- x² – 2xy + y² (1) Lim (х,у) > (0,0)( X#y ху — у- 2х…

A: We have to find the limit of the following function

Q: 2x Sí“(2t-2)² dt (a) Find the limit (if exist): lim 1 2х-1

A:

Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.