Find the constants "a" and "b" so that the following function sin 2x, if 0

Q: V1– 3x, if x -1 2x +1 Show that f is continuous at x = -1 is differentiable there by computing the…

A: See below the calculation

Q: пу Show that if y = ax" where a is a real number and n E N, then dx where x + 0. 1 Given that f(x)…

A:

Q: Use the definition of the derivative, f'(x) = lim z+h)-(2) to findf' (x) where f(x) = x³ +1. h→0 O…

A: fx=x3+1

Q: 26. Show that the function has removable discontinuity at the origin sin 2x 2x f(x) = {Z 1 if x = 0…

A: Given f(0)=1 now we have find   limx→0f(x)=limx→0(sin2x2x)=1  ( By property)

Q: 4. Consider the function f(x) = Vx – I (a) Use the limit definition of derivative to find f'(x)

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Q: the

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Q: Use the Quotient Rule to show that the Powers of x Rule applies to negative integer powers. That is,…

A:

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: 2. Find all x values on the graph of f (x) where the tangent line is horizontal for each of the…

A: To find: The values of x on the graph f(x) where the tangent line is horizontal. Given information:…

Q: . Show that the following function is differentiable everywhere on R but of which the derivative is…

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Q: I. Find the derivative of the following functions using the limit definition. Show your solutions. (…

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Q: Hiwofind the derivative of the function fwith respect to Vaniable t,, tz when ti-l, tz=3 2. X=Lncti)

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

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Q: Differentiate the following implicit function with respect to x: xy² -;=- cos (y?) a.

A: SINCE YOU HAVE ASKED MULTIPLE QUESTIONS IN SINGLE REQUEST, WE WILL BE ANSWERING ONLY THE FIRST…

Q: The limit cos(x) – 1 lim с — 4т represents the derivative of some function f (x) at some number a.…

A: This question is about finding derivative about a point .

Q: Let f(x) be a function that is differentiable at x = -2. Given that f'(-2) = 3 and f(-2) = 6, find…

A: Given data: f'(-2) = 3 x1 = -2 f(-2) = y1 y1 = 6

Q: / f'(x) sin x dx = 8, / f(x) cos x dx?

A:

Q: Consider the function f(x) = Va, x > 0. Use the limit definition of the derivative to compute the…

A: Given,           The function is fx=x , x>0We know that,           The derivative of the function…

Q: Use the first derivative test to find the local extrema of the following function: f(x) = sin x –…

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Q: Use the definition of a Derivative to show that the function is not differentiable at x = 1. Why is…

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Q: Find the intervals in which the function f(x)=sin (log,x)+cos(log,x)is decreasing.

A: By the first derivative test, a function is decreasing if its derivative is less than zero.

Q: Find tangent line for the following f(x) = ( 4x² – 3)² f(x) = sin(8 x) at (7, 0) and (T, 1). 9. at…

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Q: Find the absolute extremum f(x)=sinx    (30,120)

A: Given function is Differentiating with respect to x, we get Firstly, we find critical points of…

Q: On the graph of f(x) = tanx and the interval [ − π, π ), for what value(s) of x does f(x) = 1?

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Q: Write the interval of continuity for the function below: tan(sin(x)) log3 (7) f(x)= = for 0 < 2T

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Q: For x > 0, find f'(x) where f(x) = x*¯+3) via logarithmic differentiation. Show all ur work.

A: Topic:- application of derivatives

Q: (b) y = tan x

A: Use limit method of derivative

Q: Suppose that  f is a twice differentiable function (the function has a second derivative…

A:

Q: Determine whether the following statements are true or false:  1. ln(x')=[ln x]'  2. any continuous…

A: The given statement is,

Q: Differentiate the following implicit function with respect to x: xy - -- cos (y*) a.

A: Solving the first part: Given:

Q: 5. Find all x-values in which your function has horizontal tangent lines, f(x) = 2 sin x + x. given…

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

Q: Find the relative extrema (if any) of the function f(x) = sin 2x ; over the interval (0, π).

A:

Q: Express the limit as a definite integral on the given interval. x₁* lim Σ -Ax, [1,4] n10 (x)² + 7 i…

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Q: f (x) = -1 -1+ x + 4x² cos (:) når x # 0 når x = 0.

A: Consider the given function:

Q: f (x) = 4 sin(3x + 7) is continuous at every point x = x0; that is, lim 4 sin(3x + 1) = 4 sin(3xo +…

A:

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

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Q: Suppose that g: R →R is a differentiable function, with derivative g'(x)=(x – 1)·(x – 2)² - (x – 3)³…

A:

Q: x20 is continuous at x-0, then a = a+sinx If the function f(x): 2+2acosx x<0 a. 1 b. -1 O c. 2 d. -2

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Q: Use the limit definition of the derivative to find the slope of the tangent line to the curve f(x) =…

A: The given function is f(x)=5x2 at x=3.

Q: 5 f(x) %D sin x

A: Given  f(x) = 5sin x We have to check the continuity of the function on the interval [0, 2π].

Q: Let S(x) = { sin (2) if r#0 if r = 0. if x 0 Is f differentiable at 0? If so, find f'(0). Justify…

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Q: 3 Find f(x) if f(1) = 1 and the tangent line at (x, f(x)) has slope f(x) =

A: on solving this we get the

Q: Differentiate each of the following functions with respect to x. 13. f(x) = sinh(In x) 14. f(x) =…

A:

Q: Express the limit as a definite integral on the given interval. lim [9(x;)³ – 9x;14x, [2, 8] i = 1…

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Q: Show that the following function is continuous at x = 1 for all values of p. (px + 1, if x > 1 f (x)…

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Q: Q1) A) Find the tangent equation for the function: f(x) = Vx² + 5 at =2 ? B) Find the limits by…

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Q: Define h(x) = x° sin(1/x) for x # 0 and h(0) = 0. Prove that h is differentiable at x = 0, and find…

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Q: Write the interval of continuity for the function below: tan(cos(x)) log6 (7) f(x) = for 0x< 2π

A: The given function is: f(x)=tan(cos(x))log6xπ

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.