cos x if x + 0 8(x) = 2x if x = 0. a

Q: Locate discontinuity of the function f(x) = ln(tan2 x)

A: Given data: The expression for the given function is f(x)=ln(tan2x). Assume u=tan2x and the domain…

Q: sin x Let g(x) = . 1 Find the derivative a'(x). dt . 2 1+t3 cos? x 1+ sin x sin x 1+ cos³x cos X 1+…

A:

Q: . Power Rule for negative integers Use the Derivative Quotient Rule to prove the Power Rule for…

A: We write x-m as 1/xm, then we use the quotient rule.

Q: Determine the following limits analytically.

A: Given that : The limits is limh→0 sin(x+h) - sin xh , where x is a constant .       i

Q: See the question as attached here

A: we have to prove that  ∫1lnxdx does not have an elementary antiderivative given ∫exxdx does not have…

Q: QI) The function f (x) called invariant under differentiation opcrator function (IUDO. function) if:…

A: Proof is given in step-2

Q: What is the First Derivative Test used for? Testing where a continuous function is differentiable. O…

A:

Q: | sin x| | sin x| а. lim b. lim x→0 sin x x→0+ sin x

A: Here we will find the given limits,

Q: 48. Continuous Function Find a value for a so that the function | 2x + 3, xs 2 f(x) ax + 1, x>2 is…

A:

Q: Use the table to find the indicated limit.

A: Given tabular data is

Q: Using a method show in class, find the intervals on which fis increasing and the intervals on which…

A: Solution:  Increasing and decreasing of a function

Q: Continuity of Functions on an Interval Determine if the given function is continuous on each of the…

A: topic - functions and continuity

Q: Use the table to find the indicated limit.

A: The limit L of a function at x=a is the value that a function approaches from both left-hand side…

Q: Discontinuous composite of continuous functions Give an example of functions ƒ and g, both…

A: Given Functions ƒ and g, both continuous at x = 0

Q: Continuous Function Find a value for a so that the function - 1, x<3 [x² f(x) = \ 2ax,

A: fx=x2-1,     x&lt;32ax,        x≥3 Since the given function is a polynomial function for all x&lt;3…

Q: (Fixed-point property) Show that if f is continuous on [0, 1] and 0 < = c. (Hint: Problem 1. f(x) <1…

A:

Q: Inverse Functions Verify that f(x) = 2x + cos x has an inverse and find (f-1)'(1).

A: Given: f(x)=2x+cosx

Q: econd differentioble function and fol-b. Let ļ be a lo) Prove that fu bsinx+a cos x

A:

Q: x2 – 1 - ind the domain of the function f(x) cos² (x) + 1

A: The given function is:fx=x2-1cos2x+1To find its domain

Q: (a) Show that the tangent function f(x) = tan z is one-to-one on (–x/2, 7/2); its inverse defines…

A: a)    f(x)=tanx,  -π2,π2f'(x)=sec2x&gt;0 for x∈-π2,π2that means f(x) is strictly increasing in…

Q: Making a Function Continuous Find all values of the constant a such that f is continuous for all…

A: fx=axtanx,   x≥0a2-2,  x&lt;0 Given function is continuous for all x&lt;0  &amp;  x&gt;0. Let us…

Q: Even and Odd Functions (a) Show that the derivative of an odd function is even. That is, if f(-x) =…

A: To show that the derivative of an odd function is even (i.e) If f(-x)=f(x), then f'(-x)=f'(x) By…

Q: Identify the open intervals on which the function is increasing or decreasing. (Enter your answers…

A: we have given functionfx=x+2cosx       0&lt;x&lt;2π

Q: ´sin x-sin x cos x lim x2

A: This can be evaluated as follows:

Q: Continuity At what points of ℝ2 are the following functions continuous? g(x, y) = ln (x - y)

A: Given function: gx,y=lnx-y Here the  function is the composition fpx,y Where, the value of…

Q: Trigonometric limits Evaluate the following limits or state thatthey do not exist. (Hint: Identify…

A: limx-&gt;π2cos xx-π2

Q: Continuity. Find out, and give reason, whether f(z) is continuous at z = 0 if f(0) = 0 and for z #0…

A:

Q: sin h Let f(x) = sin x. Show that: S(x+h)-f(x) - sin x • 1-cosh = co This formula will be used…

A:

Q: sin x + 2 What is the domain of f(x) = and where isf continuous? %3D X-8 The domain of f(x) is…

A:

Q: Even and Odd Functions…

A: If f is an odd function we get, f(-x) = -f(x) Then we get, f(x) = -f(-x) Taking derivative with…

Q: Prove the identity. Cosh(-x)  = Cosh x (This shows that Cosh is an even function.)

A: To prove: cosh-x=coshxWe know that, coshx=ex+e-x2 Now, replacing x with -x…

Q: sin(x+)-sin 2. lim 2.

A: Here We have to find the limit.

Q: Calculating limits The following limits are the derivatives ofa composite function g at a point a.a.…

A: limx→04+sinx-2x a. It can be written as, limx→04+sinx-2x=limx→04+sinx-4+sin0x-0 Now comparing with…

Q: sin x Find the Maclaurin polynomial of f(x)

A: given function sinxx which is indeterminant formtherefore  consider f(x)=sin x and g(x)…

Q: Trigonometric limits Evaluate the following limits or state thatthey do not exist. (Hint: Identify…

A: Given,limx→π4tan x-1x-π4

Q: Graph of f(x) Graph of / A 1. In the interval 0<x< 1 of the first derivative test, f(x) is Ⓒa.…

A:

Q: Continuity of compositions Find functions ƒ and g such that each function is continuous at 0 but ƒ ∘…

A: Find functions f(x) and g(x) which are continuous at x=0 but f(g(x)) is discontinuous at the same.…

Q: Prove the identity. cosh(-x) = cosh(x) (This shows that cosh is an even function.) cosh(-x) = | |…

A: we have to find

Q: In Problems 115–118, graph each function. Based on the graph, state the domain and the range, and…

A: Given: graph each function. Based on the graph, state the domain and the range, and find any…

Q: За? — 6х + 7 - g(x) x2 + x + 1

A:

Q: Composition containing sin x Suppose ƒ is differentiable on[-2, 2] with ƒ′(0) = 3 and ƒ′(1) = 5. Let…

A: Given f'0=3, f'1=5 and gx=fsinx. Chain rule of differentiation states that: ddxfgx=f'gxg'x…

Q: (sin (-) x 2 Carefully sketch a well-labeled graph of f. a. State and classify all discontinuities…

A:

Q: (5 points) Find f if f"(x) = 2 + cos(x), f(0) = 10, ƒ(r/2) = -5. %3D f(x) =

A:

Q: Limits of functions Evaluate the following limits.

A: limx, y→0, πcosxy+sinxy2y

Q: Prove the identity. cosh(-x) = cosh(x) (This shows that cosh is an even function.)

A:

Q: Limits involving trigonometric functions Evaluate

A:

Q: Continuity of Functions at a Point Determine if the given functions f(x) are continuous or not at…

A: According to question,Given Function,fx = x2 + 2x +1 at x = 2

Q: Continuity at a point Determine whether the following functions are continuous at a. Justify each…

A: a) Given: f1x2=3x2+2x+1x-1 at the point a=1,  f1=312+21+11-1      =70 Therefore, f1x2 is not…

Q: DIFFERENTIATION OF INVERSE TRIGONOMETRIC FUNCTIONS 3.) y'of y = In x+1 by logarithmic…

A: Differentiation

Q: Determining unknown constants Let 5x - 2 ifx 6 1 glx2 = ca if x = 1 ax? + bx ifx 7 1. Determine…

A: Given that, gx=5x-2        if x&lt;1a                if x=1ax2+bx    if x&gt;1

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.