Sketch the graph of a function that satisfies the given f is odd, f"(x) > 0 for 0 3, f'(x) > 0 for x > 2, lim f(z) = -2

Q: Sketch the graph of f (x) = sin x on [0, π,] and guess the value of f ' (π,/2). Then calculate the…

A: Plotting: y=sinx, 0≤ x≤ π

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: ) The tangent line to y = f(x) at (-5, 2) passes through the point (-7, -5). Compute the following.…

A:

Q: Q7 Show that f is continuous on (-∞, 0) sinxif x - 4

A: Trigonometric function with sine and cosine in continuous in its domain.    Here in this question,…

Q: limit

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Q: why is the limit as x approaches 0 equal to 1/5 in the equation: ((sinx)/(5x))

A: The given limit is,

Q: Show that no tangent line to the graph of f(x) = tan x has zero slope. What is the least slope of a…

A: Slope of tangent line to f(x)=tanx is given by f'(x)=sec2(x). sec(x)≠0 , so f'(x)≠0  This proves…

Q: Find local maximum or local minimum of f(x)= -sin 2x -x defined on 22

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Q: find the tangent line of f(x)= 3x-4/x+1 at x=0

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Q: limit x approaches 0, (xcot2x)

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

Q: What is the limit of (sinx)/x if x approaches to 0?

A: Given: A function limx→0sin xx and x approaches to 0. Since sin xx is an intermediate form of type…

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: Use the limit definition of the derivative (as demonstrated on the left) to compute the exact…

A: We have to compute f'(1) using the limit definition i.e. the derivative of the square root function…

Q: Find the equation of the tangent line to the graph of f(x) = In(-x) at x = x0 = -e". %3D Equation:

A: To find the equation of the tangent line to the graph of: y=f(x)=ln(-x) at x=x0=-e4 The equation of…

Q: lim as x-->0  of (x+1-cosx)/x

A: The given limit of the function:

Q: 1 () X. lim х+ sin X→+∞

A: The objective of the question is evaluate the limit of the given function.

Q: Please help. *Find the equation of the normal line (NL) to the graph f(x)=x³-4x at x = 3. *For…

A: To find the equation of normal line to the curve

Q: limit as x---3 for the function (x-2)^11/(3-x) using L'Hopitals.

A: Consider the given function (x-2)11 / (3-x).

Q: 4. Use L'Hopital's rule to evaluate sinh(2) lim x+0 sec(x) - 1

A: we have to evaluate  limx→0sinh2xsecx-1=00 It is known that ddxsecx=secx tanxddxsinhx=coshxddxtan…

Q: Express the limit as a definite integral on the given interval. n X;* -Дх, [1, 9] lim (x;*)² + 4 n-…

A: limn→∞∑i=1nxi*xi*2+4∆x,    1, 9 Here, fx=xx2+4, a, b=1, 9

Q: tan2 (3 + Ax) – tan2 3 lim Ar 0 Ax

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Q: 1. Express the limit as a definite integral on the given interval. Xi lim Ax, [1, 3] '(x;)² +13 n00

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Q: Express the limit as a definite integral on the given interval. lim -Дх, [1, 4] (x;")² + 9 i = 1 dx

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Q: Identify the limit that represents the limit definition of the definite integral ∫39 6x3 dx using a…

A: From the given indefinite integral, observe that f (x) = 6x^3, the lower limit and upper limit is 3…

Q: The derivative of the function f (x) 3x tan x is Select one: O f'(x) = 3 tan x + 3x sec² x O f'(x) =…

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Q: Find local maximum or local minimum of f(x) = - sin 2x -x defined on 2'2

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Q: Could the limit as xà1 of f(x)=(x+sinx)/(1+x+cosx) be found simply by substituting 1 into the…

A: Given function f(x)=(x+ sin (x))/(1+x+ cos (x)) Now we will evaluate limit of f(X) as X tends to 1…

Q: Find the limit as x-->0 of sin(-3x)/sin(2x)

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Q: Express the limit as a definite integral on the given interval. lim 21 (x)2 + 7 Ax, [1, 8] dx

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Q: 2. Find the derivative of f(x) = -4x2 + 3x + 2 from first principles (i.e. the limit definition of a…

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Q: 4. Show that the function is continuous on (-00, 0). f(2) = {0 x* sin(1/x) if x 01 if x = 0 S

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Q: What is the limit (as x approaches 0) of (sinx-tanx)/x^3?

A: lim sin x -tan xx3=lim sin x -sin xcos xx3=lim sin x cos x -sin xx3 cos x =lim (sin x x cos x)(cos x…

Q: lim(cos' x+sin 5x) tan 3x x→0

A: Given- limx→0cos3x+sin5x2tan3x To Find- The value of the above limit.

Q: 2. Is the function f(x) =² continuous on the closed interval [-1, 1] ? Draw its graph illustrating…

A: Given problem:- Is the function ƒ(x) = 3/x continuous on the closed interval[−1, 1]? Draw its graph…

Q: 4) Use the Limit Definition of a derivative to find f '(3) if f(x): %3D 5-x

A: Given:- f(x) =2/(5-x)  To find:- Use limit Definition of a derivative to find f'(3)

Q: Sketch the graph of a differentiable function y f(x) through the point (-2,2) if f'(-2)=0 and…

A: Given: To sketch the graph of the differentiable function function y=f(x) through point (-2, 2) if…

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: 3. What are is the absolute maximum of f (x) = sin(x) cos(x) on the interval [0, ¤]?

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Q: lim x→0 for sin(4x)/3x

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Q: limit as x approaches infinity of (-1)x+1

A: Apply the limit.

Q: Find the limit of sec x as x approaches x lim sec x x->0

A: Topic = Limits

Q: It is defined as the limit of the ratio of the change in a function to the corresponding change in…

A: Given : what is defined as the limit of the ratio of the change in a function to the corresponding…

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: Find all points on the graph of the function f(x) =2 Sin x + Sin2 xat which the tangent line…

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Q: generate a continuous and differentiable function that is decreasing at -6, has a local minimum at…

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Q: Find the function f(x) whose derivatives is sin x and whose graph passes through the point (0,2).…

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Q: 3. Write equation of the tangent line to the graph of the function f(x) = ecosx at one of the values…

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Q: Express the limit as a definite integral on the given interval. lim [9(x*)³ - 2x*JAx, [2, 9]

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Q: What is the limit as x approaches 0 of 2x/sin(x)

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Limits

When it comes to calculus, limits are considered to be a very important topic of discussion. The main importance of limit lies in expressing the value of a function as it gets closer to a certain value. Also, limits can help you to understand other topics, such as continuity and differentiability better. In a broader sense, every calculus notion is a limit. Other branches of calculus have also been derived from limits.