1. Consider the function Y= Sin(5x) on the 0

Q: 2. dy sin x - y where f(n) = 0. %3D dx

A:

Q: Find the points of inflection and discuss the concavity of the graph of the function.

A: For a given function f(x) the critical point are the value of x at which the derivative of f(X)…

Q: 4. How many fixed points does the function T(x) = tan(x) have? %3D

A: for fixed point f(x) = x x = tan(x)

Q: Let z be defined implicitly as a function of x and y by the equation dz 4+ In (xy²) – cos (xy – 2) =…

A: Given: Let z be defined implicitly as a function of x and y by the…

Q: .Find the estimate for the root of f(x) = sin x + cos (x² + 1) – 1using Bisection methodx, = 1. 5,…

A:

Q: Find the absolute maximum and minimum values for f (x, y) = 5 sin(x) + 10 cos(y) on the rectangle R…

A: Answer is given in next step.

Q: what is the absolute extrema point(s) of f(x) = e1-cosx on [ -pi/2 , pi ], if there are any?

A:

Q: * 3x ], the x-coordinates of the points on the graph of the function f(x) = 1 + cos x where the…

A: For horizontal  tangent dy/dx=0

Q: Let f(x)= 9 sin x/ 2 sin x + 4 cos x Then f'(x)= The equation of the tangent line to y=f(x) at a =…

A:

Q: 1. Determine the absolute extrema of f(x) = (cos x − 1) sinx on [0, π], if they exist, and identify…

A: As per our policy, we are allowed to attempt only first question. Kindly post remaining question…

Q: A function is given by f (x) = x³ (2.3 sin x – 5 cos x). Compute the root between a = 4 and b = 6…

A: We have to find the root of the following function between a=4 and b=6 using Bisection method,…

Q: Consider the equation below. f(x) = 2 sin x + 2 cos x 0 ≤ x ≤ 2? Find the local minimum and maximum…

A: Given,          fx=2sinx+2cosx ; 0≤x≤2π

Q: 13. Determine where the graph of the function fíx) = sin 9x is concave upward and where it is…

A: We have f(x)=Sin(9x) , 0≤x≤2π9. To check the concavity of f we need find the value of f''(x) and…

Q: 3) If f is continuous everywhere and | f(x) dx = 6, find sec" 2x · f(tan 2x) dx.

A: d/dx(tanx)=sec^2x Tan (pi/4)=1

Q: Determine the points in the interval (0, 2n) at which the graph of the function below has a…

A:

Q: Consider the function f(x) = cos x − 3x + 1. Since f (0)f() <0. f(x) has a root in [0]. If we use…

A:

Q: The base of a three-dimensional figure is bound by the graph y = sin(x) + 1. Vertical cross-sections…

A: Given the base of 3-D figure is found by y = sin(x) + 1. The cross sections are vertical and…

Q: Find minimum of sin(x + 3) – sin(x + 1) – 2 cos(x + 2) where a E R.

A:

Q: 19. Find the points of inflection on the graph of f(x) = x+2 cosx on the interval [0, 27].

A:

Q: 4. How many fixed points does the function T(x) tan(x) have? %3D

A: As per our guidelines, we suppose to answer only one question. Here question 4) is answared.

Q: Find a and b which make the following function differentiable at x = 0; ax+b, x < 0 sin x, f(x) = =…

A: We know a function is differentiable if and only if Right hand derivative and left hand derivative…

Q: 9. Differentiate y = cos(x3/2 In x), do not simplify. x2-4 Using Calculus, show on which intervals…

A:

Q: 1 Estimate the error if P3(x) = x - x³/6 is used to approximate the value of sin x at x = 0.1.

A: We have to find the error.

Q: 35. Does the graph of Sx*sin(1/x), x + 0 f(x) (o. x = 0 have a tangent line at the origin? Give…

A: Given: fx=x2sin1x,x≠00,x=0

Q: - cos (3.xz) = 5 defines z as a function of x and y. Differentiate implicitly to Assuming y az find…

A:

Q: Find all local minimum and local maximum value(s) of the function. f(x) = 2 cos x – sin? x, 0< x< 27…

A: Option 4

Q: Find the absolute extrema of the function on the closed interval.                         y = 3 cos…

A: The given function is y=3cos x on 0,2. Compute the critical points on the given interval as follows.…

Q: Is the function h(x) = 3 cos x+ sin x concave up or down at the point 3 я?

A: Given:

Q: 1. Determine the absolute extrema of f(x) = (sin x – 1) cos x on 2' 2 if they exist, and identify…

A: Given:-f(x)=sinx-1cosx,        x∈-π2, π2f'(x)=sinx-1ddxcosx+cosxddxsinx-1…

Q: Find the absolute extrema of the function on the closed interval. y = 9 cos x, [0, 2n] || minimum…

A: The first and second derivatives of the given function, f(x)=y=9cos(x), will  be given by:…

Q: Consider the functions h : R→R and g : R -R defined by h(x) = 72 (5 + arctan(sinh 4æ)), . g(x) = 144…

A: Using inverse trigonometric  function properties

Q: 2. For the function f(x) : = sin x. Show with the aid of the elementary formula. 1 1 (1- cos 2A)…

A:

Q: Find the absolute minimum and absolute maximum values of f on the given interval. ft) = 4 cos(t) + 2…

A: This question is related to trignometry, we will solve it using differentiation.

Q: Consider the function f(x) = cos x − 3x + 1. Since ƒ (0)ƒ () <0. f(x) has a root in [0]. If we use…

A:

Q: Use the Intermediate Value Theorem to show that f(x) = 2+ sin r 3 tan x has a | (0. ). solution in…

A:

Q: Let f(x) Then f'(x) = 3 sin x 6 sin x + 2 cos x m = The equation of the tangent line to y = = f(x)…

A:

Q: y for the function f(x)= cos [x*sin (x²+1)] =, CoS 1/2 %3D ..…

A: The given function is fx=cos3x3sin12x2+1. Obtain the derivative as follows.

Q: 1. Determine the relative extrema of the function y = 2 cos x + sin 2x on the interval (0, 2Tt). %3D

A: To find the extrema of the function

Q: 1. Consider the function f defined on [0, ∞), 1 f(x) = sin- x + 0 x = 0

A:

Q: 5. Find Oz дz дх and if x - z = arctan(yz) defines z implicitly as a function of x and y. ду

A:

Q: f(x) is a sin function with amplitute 1, and is such that f(0)=0 f(1)=0 f(x) >= 0 for x element…

A: f(x) is a sin function with amplitute 1, and is such that f(0)=0 f(1)=0 f(x) &gt;= 0 for x element…

Q: 1. Find the value/s of b such that the function ƒ is continuous everywhere. f(x) = {6x – sin bx 0 <x

A:

Q: Suppose that the tangent line to the graph of y = f(x) at x = 2 is y = 4x – 3 and that the tangent…

A: The given tangent line to the graph of y=fx at x=2 is y=4x-3 and the another given tangent line to…

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

A: Given function:

Q: 5. (a) A company manufactures cylindrical metal drums with open tops with a volume of lcubicmeter.…

A: Given functions are y1=sinx; y2=sin-1x; y3=cosx; y4=cos-1x; y5=tanx; y6=tan-1x; y7=2+x+23; y8=x2-4;…

Q: Is there a value of c that will make sin² 3x f(x) = C, x = 0 continuous at x = 0? Give reasons for…

A:

Q: The graph of f(x) = cos x and a tangent line to f through the origin are shown. Find the coordinates…

A: