Let f (x)=x²-2x + . Find the slope of the graph y = f(x), at point P- (0,7) evaluating th'e limit AX im %3D Justify

Q: find the limit as x approaches 1 from the right of  ln(x^9-1)-ln(x^7-1) using L'Hospitals' rule

A:

Q: The hyperbolic cosine function, denoted cosh x, is used to model the shape of a hanging cable (a…

A: Given information:Tyhe given function is cosh(x).

Q: Find the limit. sin (3y) lim 4y

A:

Q: Find the limit using lim sinx 1. X-0 x 5) lim sin(sin x) x0 sin x A) -1 B) 1 C) does not exist D) 0

A:

Q: Find the limit: limit of 1-cos3x/cos5x-1 as x approaches 0

A: Given,

Q: limit x approaches 0, (xcot2x)

A: Limit x-> 0 ( x/tanx ) =1Calculating the limit of the given expression using this result:

Q: Let f (x) = x² – 4. a. Find f'(x) using the formal limit definition of derivative. -

A: The formula of formal limit definition of derivative is  : lim h →0  [{f(x+h) - f(x)} / h ]

Q: the derivative of the function by the limit process. f(x) = x²+x-3

A: Topic:- limits and calculus

Q: Estimate the limit numerically (or graphically). Use oo or -oo for too. Write DNE if the limit does…

A:

Q: 2. Show function f(x,y) = does not have limit of a function at point (0,0). 2² + ?

A: We need to show that the function does not have limit at point (0,0)

Q: B) Find the limits by using L.Hopital rule : 7x 1. lim x→0 sin 2x

A: Here we will find out the required value.

Q: 32? And are

A: {x2                               if x<-2f(x)={x1/5                           if…

Q: In terms of limits, what does it mean for ƒ to grow faster than g as x→ ∞?

A: Suppose we need to find out limits  And f(x) grows faster than g(x), Then denominator gets much…

Q: find the limit. limit as x approaches 0 sin23x/x2

A: Apply the limits and find the in-determinate form.

Q: ) Let f(x) = 3x – 1. Use the limit definition of the derivative to find f'(x). %3D (3 Marks)

A: Answer - definition of derivative f'(x) = lim h tends to 0 ( f(x+h) -f(x) ) /h

Q: 1. Find the derivative of f(x) = 2. at x = 0 using the definition of the derivative as a limit. Va +…

A:

Q: Find the limit. lin x->∞ arctan(ex)

A: Given: limx→∞tan-1ex for evaluating this limit have to use  limx→∞ex=∞

Q: (a) Let f (x) = Vx – 1. Use the limit definition of the derivative to find f' (x).

A:

Q: Find two paths of approach from which one can conclude that the function has no limit as (x, y)…

A: To find two path of approach for the given function such that we conclude that no limit exist when…

Q: Estimate the limit numerically or state that the limit doesn't exist: sec-{z) lim z¬1+ vz²-1 (Enter…

A:

Q: e limit of

A:

Q: 6. Calculate limit: lim tg x X→0 2-V4+3x

A: Here we have to calculate Limit =limx→0 tgx2-4+3x

Q: 5. Use the limit definition of the derivative to find the derivative of f(x) = 3x-2. f(x+h) - f(x)…

A: f'(x)=limh→0 f(x+h)-f(x)h

Q: Evaluate the limit as x approaches infinity of (x2 - ln(3/x)) / 4x2+6x

A:

Q: Find the limits limx→0+x-1/ln x

A:

Q: limit

A:

Q: Q3 :(A): By using "L' Hopital rules "; Find the limits of : (1) limx-ol: 1-cos x - sin²x

A:

Q: Use L'Hospital's rule to evaluate the limit sin(3t) dt lim X-0 x2 O O

A: We have, limx→0∫0xsin3tdtx2 On solving further the integral part, we get the result as…

Q: 2 Find the derivative of f(x) =x² – 6 from limit definition. - Show all steps of working. f(x) :…

A:

Q: Let f(x) = 1- 5x2. Use the limit definition of the derivative to show tl f'(x) = –10x

A:

Q: Q1) A) Find the tangent equation for the function: f(x) = vx2 + 5 at =2 ? B) Find the limits by…

A:

Q: Use logarithmic differentiation to find for y = x4* %3D dx 2x Use LaHopital's rule to calculate the…

A:

Q: Find the limit of xsinx as x approaches 0

A: Given:

Q: How do you approximate a limit numerically AND graphically?

A: We always evaluate limits from both the left and right directions and if they match, then, the limit…

Q: (sin 2x)* - 4x →0+ x -

A:

Q: Compute f'(3) using the limit definition of derivative if f

A: Given: f(x)=6x2f'(3)

Q: 4x2 [cos (2)* 1. lim X→+00 Find the limit using L'Hopital's Rule

A:

Q: (B) Let f(x) = 3x – 1. Use the limit definition of the derivative to find f'(x). %3D

A: Explanation of the answer is as follows

Q: Find the limit by rewriting the fraction first. x- y + 5/x - 5Vy lim Vx - Vy (ху) -- (0,0) x#y x- y…

A: limx,y→0,0x-y+5x-5yx-y =limx,y→0,0x-yx+y+5x-5yx-y =limx,y→0,0x-yx+y+5x-yx-y

Q: Find the limit of tan^-1(e^(x^2)+x^2+1/x) as x approaches negative infinity

A:

Q: Estimate the limit numerically or state that sec (x) lim x→1+ vx³–1 (Enter DNE if the limit doesn't…

A:

Q: Find two paths of approach from which one can conclude that the function has no limit as (x, y)…

A: The given question is related with limits. Given that fx , y = 3y9x2 + 4y2 . We have to find two…

Q: 2) Use the definition of the derivative f(x+h)-f(x) lim hー→0 to find the derivative of f(x) =…

A: Our objective is to find the derivative using definition.

Q: 2. Find the horizontal asymptotes of the graph f(z) = %3D 3. Differentiate f(x) = – using the limit…

A: 2. To find the horzontal asymptotes of the graph f(x)=x2-2|x|3+13.  To find the derivative of…

Q: Limit x approaches to + infinity 3x+1 ÷ 2x-5

A: To evaluate: limx→∞3x+12x-5 Solution: Here,limx→∞3x+12x-5 On simplifying further we get:…

Q: limit x to infinty tan(5t)sec(99t)/t

A: Lim           f∞(st) Sec(q q t )tx→∞    Here limit x→∞ But the function is in t ∴

Q: Find the solution to the equation 2x² - 4x + 1 = 0 using simpsons rule with an lower a and upper…

A: Given , f(x)=2x3-4x+1 we have to use Simpsons rule to find solution with lower limit is 1 and upper…

Q: Let f(x) = ln x / sin^-1 x    analyze the limit : lim x--> 1- (from the left) f(x)

A: Given information:The given function is

Q: lim (x²Vx* – 1 – x*)

A:

Q: Estimate the limit numerically or state that the limit does not exist (DNE): sin(7x) lim x →0

A: Given: