Let f(x) = . Calculate the difference quotient %3D х-4 f(1 + h) – f(1) h for h = .1 -0.114 h = .01 -0.111 h = -.01 -0.110 h = -.1 -0.108 f(1 + h) – f(1) lim h→0 h -1/9

Q: If V 16x <f(x)sx+4 for all positive x-values, then what is lim f(x)?

A:

Q: In the function:  f(x)= (3x^2)ln(x) , x&gt;0 What are the vertical asymptotes?

A: Given function is,

Q: Q3: A) Find the limits below 1) lim (x,y)—(0,0) x² + sin²y 2x2 + + y²

A:

Q: Q3) Using the definition, lim f(k+h)+f(k) h-0 ds calculate the derivatives dk h of the function : k…

A:

Q: In x lim T00 rm m > 0 is

A:

Q: find the limit of g(x) as x approaches the indicated value.

A: ltx→-25-x2gx=0As x tends to -2 denominator tends to 1 .    gx≠0 . gx&gt;0

Q: Find the value of the limit lim SINX X 0 2x 02x (a) 0 (b) 1 (c) 1/3 (d) 1/2 (e) 1/4

A: Here we have to find the limit of the function. In the first step use the property of the limit:

Q: (a) Find the exact value of the overshoot lim E 1/1- dx/x?

A: Given limn→∞∑j=1n1/j2-∫1πdxx2

Q: 2. Use a table of function values to estimate lim in3x sin 3x sin3x -0.1 0.1 -0.01 b. 0.01 -0.001 c.…

A:

Q: Find the limit. cos(x) – 1 +x2 lim x-0 2x4

A: It is given that, limx→0cosx-1+12x22x4.

Q: Find the limit of the exercise below.

A: Factor the numerator using a^2-b^2=(a+b)(a-b) formula. With a=t and b=4

Q: lim 4 sin(x + n) + 3

A:

Q: Let f (x)=x²-2x + . Find the slope of the graph y = f(x), at point P- (0,7) evaluating th'e limit AX…

A: fx=x2-2x+1 We need to find the slope of the graph at the point P0, 1

Q: evaluate the limit:  limit of the square root of 1+t - square root of 1-t / t as t approaches 0

A:

Q: Find the Indicated Limit Limh-0(4h5-20h2+2h+1)

A: Given, Limh-0(4h5-20h2+2h+1).

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: Assuming h > 0, compute Vx - Vh lim x→h X-h (a); Vh (b). 2h (c) (d) 2h (0)

A:

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

A:

Q: 2. Use the paths x = y and x = 0 to verify the limit. lim (x.y)-(0,0) x2+y²,

A:

Q: (-1)"f" cost =1--+ 4! 2 (2n)! In(1+t) =t-+ 3 -.+(-1)*-"4 +... n Yukarıda verilen cost ve In(1+x)'in…

A:

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: 2x + 1 If t(x) find lim,-o t(x) %3D 8x + 1

A:

Q: The percentage of movie advertising as a share of newspapers' total advertising revenue from 1995 to…

A: Given that: p(t) = −0.07t + 5.0    if t ≤ 3 0.3t + 12.0if t &gt; 3

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: Use the graphs of f and g and their tangent lines at (-1,0) to find f(x) lim Number x-1 g(x) y f(x)…

A:

Q: 2-メ Compite lim %3D Xラム z(T-X)

A:

Q: Let f(x) = 3x² – 5x + 1 f(x+h)-f(x) (a) Find f'(x) using the limit definition of derivative. That…

A:

Q: Determine the 2.x2 – 4x + 6 dx using the definition. (hint: lim Rn)

A: Given: ∫12 2x2-4x+6 dx  To find: Value of the limit.

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

A:

Q: B. Calculate the limits of the following functions.. 1. limx¬-1(2X2 + X + 4) 2. limy--2(y3 + 5y – 1)…

A:

Q: 15) Annual U.S. imports from a certain country in the years 1996 through 2005 could be approximated…

A: Given I(t) = t2+3.5t+48    (1 ≤ t ≤ 9)E(t) = 0.5t2−1.4t+13    (0 ≤ t ≤ 10)

Q: For f(x)=√7x+2, find f′(x) using the definition f′(x)=limh→0f(x+h)−f(x)/h. f′(x)= Using this, find…

A: Equation of the line passing through the points x1,y1 and having slope m is y-y1 =mx-x1.

Q: Find the limit V1+t4 dt lim

A:

Q: Along the path x = e find lim (1,y)→(1,0) y2-6ry 3x-y-3 O 2 O does not exist O -3 O 3

A:

Q: If [ f(x)\dx<∞ show that limf(x)dx=0 k→∞00 1

A: We have to prove that given expression.

Q: Evaluate the limit x2 + 0x – 25 lim x - 5 x-5 Enter I for co, -I for -oo0, and DNE if the limit does…

A: we have to evaluate the following limit

Q: Use a computer algebra system to graph the function. 7xy f(x, y) = x + y2 + 6 3e+31 2.5e+31 20+31 3…

A: We have to graph the function first

Q: Consider the function 2+2+17-2ry+v² if (r, y) # (0,0) f(r,y) = if (1, y) = (0,0). (b) Find…

A:

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

A: Given:

Q: S (2t)*dt lim x→ =? х* — 1

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

A:

Q: Determine lim In/xy. (x,y)(e4)

A: lim(x,y)-&gt;(e2,4)lnxy

Q: Let F(x) = | 3e“ dt. Find lim F(x) if it exists. If the limit does not exist, explain why. x→0

A: see below the answer

Q: For f(x) = 2x³ - 2, find ƒ '(x) using the definition f '(x) = lim f(x+h)-f(x) h h→0 f'(x) = Using…

A: Let's find.

Q: Consider g(x)=−7x3+7x2+9. a) limx→0−g(x)= b)limx→−1−g(x)= c)On what interval(s) is g(x)…

A: It can be solved using the limiting definition of continuity

Q: If x Vx sf(x)s -x+ 1for all positive x-values, then what is lim f(x)?

A:

Q: thát limx,y)→(0,0) x6- dõés not exist by using the two-paths approach.

A:

Q: Find the Horizontal Asymptote(s) of f(x) = 1+

A: We have to identify the relative extrema according to the given information and find the horizontal…

Q: Compute the lim as x goes to 0+ (e^x - 1 - x)/ (xe^x - x)

A: we have to compute the limx→0+ex-1-xxex-x