Q3/Discuss the behavior of the following function as x 0: f) = sinx

Q: Graph the function y=-sin2x on [-pi,0]

A:

Q: Differentiate f (x) = sin Vx by the first principle

A: Here we use the formula

Q: (1 point) Find the derivative of the following function F(x) = (2t – – 1)³ dt

A:

Q: Differentiate f(×) = sin x from first principles

A: Given query is to find the differentiation of sin(x) from the first principal.

Q: Find the derivative of the following functions: tan (2x²-1) 1. f(x) = sin(2x²-1) 2. f(x) = sin² 4x…

A:

Q: Determine whether the point x=0 is an inflection point of the function f(x)=sinx.

A: Inflection point is the point on f(x) where the graphn changes the concavity. At this point  double…

Q: Find the derivative of the function f(x) = In(2a? + 5æ)

A: ddxln (x)=1xddxxn= n xn-1

Q: se the first principle of differentiation to find f'(x) for the function f (x)=

A:

Q: What is the first derivative of g(x) = In 4x²+4x+8 ? x 3 tan x

A: we use Logarithmic properties

Q: Find the slope of the graph of the function at the given point.

A: We have the given function as fx=4x5+3x-sinx          ⋯⋯1 As we know that, slope of a function fx is…

Q: Find the derivative  f(x)= sin 2xcos2x

A: The given function is,

Q: apply 1rt and second derivative to sketch graph  1)f(x)=3+7e^(-0.2x) and  2)f(x)=ln(2x+4)

A: In the question we have to draw the graph.

Q: Let f (x) = sin−1(x^2/6)− tan−1(12x + 1). Find the derivative of f.

A:

Q: |(9-x)³ x² – 2 9. f(x) = In -

A:

Q: f(x) = cos(IX) 2*-x f '(x)

A: Differentiation under quotient rule

Q: Consider the function f(x) whose second derivative is f''(x)=9x+9sin(x). If f(0)=2 and f'(0)=3, what…

A:

Q: 42. f(x) = In(xeV + 2)

A:

Q: Find the slope of the graph of the function at the given point. f(x) = 4x5 + 2x - sin(x), (0, 0)…

A: We havefx=4x5+2x−sinx

Q: Find the derivative f(x)= In(ex+9)

A: find the derivative

Q: 1 Find the function whose derivative is (x+1)-

A:

Q: 3 Use the definition of derivative to find f'(x) for f(x): II

A: Given:

Q: Consider the function f(x) whose second derivative is f''(x)=4x+3sin(x)   If f(0)=3  and f'(0)=2…

A: detailed solution with explanation is given below

Q: Find the slope of the graph of the function at the given point. F(x) = 4x5 + 5x - sin(x), (0, 0)…

A:

Q: What is the derivative of sin(2x) at the point (0,0)? O 2 O -2 O 4

A:

Q: В. f(x) = (sin ebx³ ). 3 |cot(26x) x4 -

A:

Q: r (4x2 – 3x + 5)* - 3.) c(x) = %3D sin x

A: solution:- find the derivative by using the quotient rule

Q: Find the 35th derivative of f(x)= sin.x.

A: Given,             fx=sinxTo find: The 35th derivative of fx=sinx.

Q: Find the slope of the graph of the function at the given point.                         f(x) = 4x5 +…

A:

Q: Consider the function f(x) whose second derivative is f''(x)=8x+10sin(x). If f(0)=3 and f'(0)=2 what…

A: The function is f"x=8x+10sinx.   Integrate the function.…

Q: Find the 56th derivative of the function f(x) = cos(x). The answer is function

A: Consider the function fx=cosx Here, the objective is to find the 56th derivative of the function.

Q: Find the first derivative of the followin the result whenever possible. V4 – x² 1.y = x arcsin=-

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

Q: Compute the derivative of each function. f(x) = [sin(4² + x)] [cos(x* + 4)] %3D

A:

Q: Find the slope of the graph of the function at the given point. f(x) = 7x5 + 8x − sin(x), (0, 0

A: solution: the objective is to find the slope of the given graph

Q: Consider the function f(x) whose second derivative is f''(x)=2x+3sin(x). If f(0)=2 and f'(0)=4, what…

A:

Q: If f(x) =>(1- (sinx)²)" .Determine the value of f)

A: use the trigonometric identities to simplify and the solve. detailed explanation is in step 2 answer…

Q: (a) By using definition of differentiation, find f'(x) when f(x)= 3x – 5x

A: Definition of differentiation statets that: f'x=limh→0fx+h-fxh (a) Given function is fx=3x-5x2 To…

Q: Consider the function f(x) whose second derivative is f''(x) = 7x + 8 sin(x). If f(0) = 3 and f'(0)…

A: Recall: ∫xn dx=xn+1n+1+c ∫sinaxdx=-cos(ax)a+c ∫cosax dx=sin(ax)a+c ; where 'c' is an integration…

Q: Find an equation of the tangent line to the graph of the given function at the specified point. x2 -…

A:

Q: Find the derivative of the function f(x) = x sin(6x + 14)+ In(5z+9) Answer:

A:

Q: Use a computer algebra system to find the derivative of the function.

A: Given

Q: B) Use the definition of differentiation to find the derivative of the function f(x) = 4- Vx + 3. Is…

A: Consider the function: fx=4-x+3 The definition of derivatives is given by the formulas,

Q: Find the derivative of f(x) = cot^−1(x^2 + 3)

A:

Q: Find the derivatives of the following function f(X) from the first principle xsinx

A: derivative of xsinx by first principl is xcosx+sinx. for this question see 2nd step.

Q: What is the 1881th derivative of the function given by f(x)=1881x + 1923 at the point x=2020.

A:

Q: Consider the function f(x) whose second derivative is f''(x)=2x+7sin(x). If f(0)=3 and f'(0)=3, what…

A: to find f'(x) integrate the given function c=integrating constant. Then plug x=0 and f'(0)=3 and…

Q: Let f(x) = 6 In(sec(x) + tan(x)) f''(x) = HINT: Simplify the first derivative before you find the…

A:

Q: f(x) = In(sin² x)

A: Given,           fx=lnsin2x

Q: f(x)=4 sin¹+x+√4x²

A:

Q: Consider the function f(x) whose second derivative is f''(x)=8x+8sin(x). If f(0)=4 and f'(0)=4, what…

A:

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.