%3D - the definition of a derivative, the derivative of f(x) = x is O a. VI+h lim h-0 Ob. lim h-0 lim h-0 Od. lim h-0 lim h-0

Q: lease kindly use chain rule on the below to find the derivative and label all parts.  h(x)= cos…

A: Given function  h(x) = cosx4

Q: Q4: a) Use the four steps rule, for find the derivative of function: 1 f (x) = x + 5 b) Find : lim…

A: Solution:

Q: f(x+h)-f(x) (10 Points) Use the definition of derivative lim h→0 to find the derivative of f(x) =…

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Q: Find the derivative of the function f(x) = x? – x at a = 3 by definition- f(a + h) – f(@) ) (Recall…

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Q: The limit below represents the derivative of some function f(x) at some number a. 2(2 + h)* – 32 lim…

A: The derivative of the function fx at some number a is given by f'a = limh→022+h4-32h…

Q: Compute the right-hand and left-hand derivatives as limits and check whether the function is…

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Q: Compute the derivative function f '(x) algebraically. HINT [See Examples 2 and 3.] f(x) = −5/x

A: Formula       f'(x)=limh→0f(x+h)-f(x)h

Q: Question Which of the following is the correct limit definition for the derivative of g(x) = 2"? %3D…

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Q: Alternative Formula for the Derivative f'(x) = lim Z-X f(z) = f(x) Z - X

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Q: Q3]a)Describe arctanh(z) in terms of logarithms. c) Find derivative of arctanh(z).

A: Given: f(z)=arctanh(z) To find: a) Logarithmic form of f(z). c) Derivative of f(z).

Q: Compute the derivative function  f '(x) algebraically. HINT [See Examples 2 and 3.] f(x) = 9x2 + x…

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Q: h. Use the second derivative to identify intervals where f(x) is concave up. (-0,3) X i. Use the…

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Q: f(x +h) – f(x) Use f'(x) = lim to find the derivative at x for the given function. h-0 s(x) = 4x + 2…

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Q: 3pts) Find the equation of the tangent line to the graph of the function f(x)=x-Vx at the point…

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Q: Use the limit definition of the derivative function to find dz

A: Given: fx=x4

Q: f(r+h)-f(x) 1. Use the definition f (x) = lim to find the first derivative for the function h0 h…

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Q: / Discuss the relationship between the derivative and (Lim) with drawing if it is required?

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Q: f(x+h)-f(x) determine the derivative/ slope of tangent for = lim h→0 h -1 2x 5a) Using the formula…

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Q: Use the definition of derivatives using this formula f(x + h) – f(x) lim h 1. Find the derivative of…

A: Given: limh→0fx+h-f(x)h y=1x-2

Q: f(x+Ax)-f(x) Ay = lim Ax-0 find the derivative of the Using = lim dx Ax-0 Ax Ax following function.…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

Q: The limit x°-1 lim x→1 r - 1 represents the derivative of some function f(x) at some number a. Find…

A: We need to find f(x) and value of a.

Q: Let f(x) = x² + [a]. Consider the definition of a derivative at a, f(x+h)-f(x) lim¬0 h Fully…

A: Given: fx=x2+a

Q: f'(x)= limh->0 (cos (h)-1)/h  this represents the derivative of a function f(x) at a number x=a,…

A: solution is given below

Q: f(x +h) – f(x) Use f'(x) = lim to find the derivative at x for the given function. h→0 s(x) = 8x + 9…

A: Given  f(x)=2x2-2x+4

Q: Jse the definition of derivatives using this formula f(x + h) – f(x) lim 3. Find the derivative of…

A: Here we use the derivative using the formula  limh→0f(x+h)-f(x)h

Q: The definition of the derivative of a function is f'(x) = lim f(x + h) – f(x) h→0 h Write, but do…

A: Given: The definition of the derivative of a function is f'x=limh→0fx+h−fxh I. fx=2xsinx II.…

Q: Determine the sign of the second derivative function as x varies. Where is f' positive? Where is…

A: As per the guidelines we can solve 3 questions only.

Q: Please show step-by-step solutions.

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Q: This limit represents the derivative of some function V16+h-2 f at some number a. State this f and…

A: Given limit as a derivative of the function limh→0(16+h)14-2h  we have to find the value of a and…

Q: The limit (8+ h)² – 64 lim h→0 h represents the derivative of some function f(x) at some number a.…

A: We will find the f(x) and a by using limit definition as shown below

Q: f(x+h)-f(x) 1. Let f (x) = Vx find the derivative of the function using the formal definition of the…

A: Given f(x)=xTo find derivative of f(x) usingf'(x)=limh→0f(x+h)-f(x)h

Q: Q8. Identify the function, whose derivative is defined below: (x + h)2 – x? dy - lim dx h→0 h A.…

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Q: ind derivative w.r.t.x: f(x)=x3 -x. Al

A: Given,         f(x)=x3-x

Q: Find the derivative of the function s(x)= √x+7/√x s'x=   *No images are included

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Q: 3. Find f'(x) using the definition of the derivative. a) f(x) = 7 lim f'(x) = b) f(x) = 3x %3D

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Q: f(x +h) – f(x) Use f'(x) = lim to find the derivative at x for the given function. h-0 s(x) = 5x + 8…

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Q: The limit below represents the derivative of some function f (x) at some number a. 4(2 + h)° – 256…

A: We use the basic definition of derivative at a point. And compare with the given limit.

Q: The limit below represents a derivative f' (a). Find f(x) and a. sin ( +h) – 1 lim h-0 h f(x) = a =

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Q: the box that minimize the amount of material used. st, find a formula for the surface area of the…

A: In this question, the concept of maxima and minima is applied. Maxima and Minima The extrema of a…

Q: Vx-1 1) Evaluate lim x→1 Vx-1 1-x 2) Find the derivative of y = arctan 1+x

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Q: f(z)-f(x) Use the formulaf (x) = lim to find the derivative of the following function. %3D f(x) =…

A: Let z = x+h where z tends to x then h tends to 0. Put z in the formula and then put value of the…

Q: f(x +h)- f(x) Lim 2. Find the derivative of the following function using the *0 Show all your steps.…

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Q: I. Use the definition of the derivative f'(x) = lim 7&+h)=Jx) to find the derivative of the…

A: Formula: limx→axn -anx - a = nan-1 Given: R(z) = 6z3+18z5-13z10

Q: The derivative of the function f(x) = -5x? – 16x + 22 by definition of derivatives f(x + h) – f(x) |…

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Q: Determine the sign of the second derivative function as x varies. Where is f' positive? Where is…

A: According to question given thatf"(x)=-4(-3x2+1)(x2+1)3

Q: Use the definition of derivatives using this formula f(x + h) – f(x) lim h 3. Find the derivative of…

A: We have,   According to the definition of derivative,

Q: 3.2 The Derivative as a Function ) Usc the Definition, f'=f(xth)- fcx), to find | ん the derivative…

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Q: Which is use to compute the derivative of a function? * f(x+h)-f(x) lim h-0 h Option 1 O f'(x)=0…

A: We can find the derivative of a function by using the limit definition.

Q: 4x Consider the function f(x) : 3 – x a. Use the \underline{limit definition of derivative} to find…

A: We can solve all these points in the following way:-

Q: Find the Derivative of the reciprocal of a function 1 working from the definition f'(x) f(x) lim fx…

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Differential Equations

Have you ever observed the movement of the satellites and rockets or how the planets go around the sun in their orbits? How will you determine their motion? Definitely they follow some scientific laws and these kinds of problems are framed as differential equations.