sin x S-9 “,x < 0 g(x) = %3D 3x,x >0 a –

Q: The function f(x) = 3x³ + cos(3ræ) + 2x , x > 1 is known to be a strictly increasing function on its…

A: Given f(x) = 3x3 + cos(3πx) + 2x,  x≥1   ⇒ f'(x) = 9x2 - 3πsin(3πx) + 2

Q: Find the value of c that makes the function continuous at x = 0. SNIPP

A: Hence it is given that the given function is continuous, so we can write:…

Q: O Find absolute extrema for f(x)= x*-6x² +9x +l in terval [0,5] Gn

A: Given that fx=x3-6x2+9x+1To find : absolute extrema on interval  0,5Solution…

Q: Let f be a function which is continuous, differentiable , and holds -1s f(x)<1 over the interval 0,…

A:

Q: FInd the intervals in which the function f(x) =sin(logex) +cos(logex) is decreasing

A: Given function is, f(x)=sin(logex)+cos(logex)

Q: Find f(x), the most general antiderivative of the function: f" (x) = 18x – 3 sin(x)

A: Explanation of the answer is as follows

Q: Find the absolute extrema of the function on the closed interval.                    f(x) = sin 2x,…

A: Approach: Without wasting any time, take the derivative of the original function. Find critical…

Q: 5x sec Suppose m' is continuous at r = 0 and m'(x) if x > 0. log3 (2.x + 1) + cosh r If m" (0) = 0,…

A:

Q: Find the intervals on which f is increasing and decreasing. f(y) = sin y - y cos y on 2' 2

A: Find your answer below

Q: Find the intervals on which ƒ is increasing and the interval on which it is decreasing.

A: Given function is fx=9-x2+sin-1x3.

Q: Find the length of the graph of f(x) = ln sec x from x = 0 to x = r/6.

A:

Q: Find the family of antiderivatives of f(x) = sin 3x.

A: Given that f(x)=sin3x      ...(1)

Q: Determine values of a and b that make the given function continuous: if x 3

A:

Q: Consider the function if x 1 Evaluate the definite integral. f(x) dx -2

A:

Q: Find the extreme values for f(x) = sin(x) + cos(x) on the interval [0, 2π].

A: The given function is f(x)=sinx+cosx   and the interval is 0, 2π. We have to find extrema on the…

Q: dy Find for the following function: dx 1- y = etan'x 2- x³y + x²y = 2 at x = 2 3- y = log4(x³ – x)

A: Finding Derivatives by applying chain rule of derivative

Q: The slope of the line normal to the graph y = 2 ln(sec x) at x = is: O-1/2 O non-existent O-2 2

A: The graph y=2lnsecx at x=π4

Q: Find of the following by implicit differentiation. Show solution. dx y sin x =x2 – 2y • sin x+ sin y…

A: This question is related to derivative.

Q: Find the extreme values of the function f(x) = sin(2x) within the interval 0 < x < 2n %3D

A: Given function f(x)= sin(2x)            0≤x≤2π

Q: S/ kx +1 O<x<1 a) Let f(x)= %3D 2x+3 13x<3 Find the value of k, given that the function f is…

A: If the function is continuous at some point , then the value of both side of function is equal .

Q: Find a root of f (x) = 3x + sin(x) – ex = 0. Use 6 iterations to find the approximate value of x.

A:

Q: Find f'( – 2) for f(x) = ln( (x* + 3)´) as an exact fraction or rounded to at least 2 decimal…

A:

Q: Evaluate the definite integral. sec (x/4) dx 0.

A:

Q: Find for the following function: dx 1- y = log2 cosh(2x) 2- y = e(x*+1) 3- xy + x²y = 3 at x = 1 4-…

A:

Q: 33 f(x) = sin 2x + Ve2x + 2x – In e, x # 1 1-x

A: derivative

Q: Q1: From the given graph of f(x) = sin x; [0 ,27] , f ind: (a)The critical points. 211 -2…

A:

Q: Let h (x) = x sin . 1. Find the x-values where h has horizontal tangent lines in the interval 0, 27.…

A:

Q: Find the constants "a" and "b" so that the following function (sin 2x, if 0<xs. sin 2x, if 0 < x < f…

A:

Q: Find the Padé approximation R1.2(x) for f(x) =(ln(1 + 2x))/x

A: Pade approximation R1,2(x) for f(x)=ln(1+2x)x…

Q: is continuous and integral 3 to 1 f(x)dx =8, show that the graph of f intersects the line y=4 at…

A: Given that f is continuous and f13f(x)dx=8 To prove line y=4 intersects the graph of f altleast can…

Q: For what x-value (approximately) does the function f(x) = sin(x) – x reach height -2? (Use a = 2 as…

A:

Q: The height of an arch above the ground is given by the function y = 11 sin x for 0sxSr. What is the…

A: This question can be solved by applying the formula of average height of an arch.

Q: Find for the following function: dx 1- y = log2 cosh(2x) 2- y = er+1) 3- xy +x*y = 3 at x = 1

A: As per our company guidelines we are supposed to answer only first 3 sub-parts. Kindly repost other…

Q: find the extreme values (absolute and local) of thefunction over its natural domain, and where they…

A: Consider the given function as y=xlnx

Q: Find the indefinite integral. ∫sec x/2 dx

A: Given ∫sec x/2 dx. We need to evaluate the above integral.

Q: Suppose that the tangent line to the graph of f(x) = x(6*) at r = 1 is equal to the tangent line to…

A:

Q: Consider the function (x if x 1 Evaluate the definite integral. •5 f(x) dx -3

A:

Q: Find a nonzero value for the constant k that makes th tan(kx) x 0 Continuous at x = 0.

A:

Q: Find for the following function: dx 1- y = log2 cosh(2x) 2- y = e(x+1) 3- xy + xy = 3 at x = 1 4- y…

A:

Q: 2) Find the domain of the real-valued function defined as f (x) = arc cos 2x/(1+x^2 )+ log…

A: First find the domain of f1x=cos-12x1+x2: The domain of cos-1x is -1,1. Therefore, -1≤2x1+x2≤1 Now,…

Q: If f(x) = sinh 2x − e2, find the exact numerical value of f"(ln 2).

A: Given : f(x) = sinh 2x − e2

Q: [ 2 sin(;) 15. Given that f(x) =- ki, is a continuous function at z = 0, the value of k is x = 0 B !…

A: A function f(x) is continuous at x=a, if right hand limit = left hand limit = function value at x=a…

Q: The height of an arch above theground is given by the function y = 10 sin x, for 0 ≤x ≤∏.What is the…

A: The height of an arch above the ground is given by the function y = 10 sin x, for 0 ≤x ≤∏.What is…

Q: Find the relative extrema of f(x) = 1/2x − sin x in the interval (0, 2pie ).

A: Maxima or minima: Let f(x) is any function. 1) Evaluate f'(x) = 0 for critical point. 2) Evaluate…

Q: Find a value of c that makes Continuous extension the function 9x - 3 sin 3x 5x f(x) = c, continuous…

A: The given function is

Q: proximation at z = 0 to sin(4r) is A + Bx where A is:

A:

Q: If f(x) = 4 cos x – 6x, find the relative percentage error in f(x) for x=0, if the error in x is…

A:

Q: Let f (x) = 2x* – 3x3 + 5x + 1. Find the value of df-1 at x = 1. dx

A: We have given function;

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.