e graph of h(x) = f(x) + g(x)

Q: Using the first and second derivatives, sketch a graph for y=x^4-4x^3+1.

A: The given function is, fx=x4-4x3+1. The first derivative of fx=x4-4x3+1 is, f'x=ddxx4-4x3+1=4x3-12x2…

Q: lim          e((x+4)/(x+2)) x->2-

A: Insert the value of given limit. The result is a finite number.

Q: finding the local mins and maximums and the intervals of increase and decrease and making a sign…

A:

Q: lim x→-0 e-x

A: Given: fx=limx→-∞x2e-x

Q: ー2 a) lim X >6 (x-6)3 b) lim E) ゼ+t

A:

Q: lim 2x'e X- | X→+∞

A: To find: The limit of a given problem

Q: 6) lim (x – Ln(x² + 1)) X - X→∞

A: Here I am attaching image so that you understand each and every step.

Q: c. lim f(x) X→-2+ d. lim f(x) X-0

A:

Q: x - 2x +x lim e) 2x+x-2x

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

Q: 4. Using the first derivative test to find the location of the local maxima of the following…

A: Given function is  f(x)= x^3 -3x^2 -9x-1

Q: limit as x approaches infinity of (e^x + e^-x)/(e^x - e^-x)

A: Consider the given expression of which limit has to be calculated:

Q: k(x) = (1+ x²)etan-(x)

A:

Q: V-x – 2 – V3 te lim x--5 -x - 5

A:

Q: 1. f(x) = 3(x + 2)(x – 3)²(x + 5) %3D - looc th e graph

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find out which graph is f(x), f1(x), f11(x) For example: Function A is f(x), Function B is the…

A: here function c the graph only passes from origin  than this is the graph of f(x).     in function B…

Q: liminate arbitrary constants y=C1x+C2e-x+x2

A:

Q: Find the limit

A:

Q: Find vertical and horizontal asymptote of F (x)=Ln(4-x^2)

A: To Determine: Find vertical and horizontal asymptote of:…

Q: lim x++∞ x² + x e²x + Inx

A: As per the company guidelines We can first question only. Please understand. Kindly repost the…

Q: Using the criterion of the first and second derivatives, find the graph of the function b) F(x) =…

A:

Q: lim +h)-f(x) h→0 >- f(x) = v5x + 1 when x %3D h 5

A: Given:  fx=5x+1x>-15 To Find:  limh→0 fx+h-fxh=?

Q: g(x) lim -2 h(x)

A: Please refer to the image below

Q: e equation implicitly defines y as a differentiable function of >

A:

Q: lim (x2 – x')e?* X -

A:

Q: e) lim e¬x²x3

A:

Q: c) lim x-0 √x+5-√√5-x x

A: Given query is to find the limit of the expression.

Q: lim (lnx/x1/2 - 1/x)  ? x-->infinity

A:

Q: (g) lim (x- Vx +x - Vx-x (h) lim 3x²

A:

Q: Using the first and second derivatives, sketch a graph for y=x^2-4x+10

A: Given equation  y=x2-4x+10 Apply power rule to find first and second derivative f'(x)=2x-4f''(x)=2…

Q: lim,0 e2x _e-2x 'x→∞ e2x+e-2x

A:

Q: 6) find the 2nd derivative and the graph Y’= 12-x-x^2

A: y'=12-x-x^2 Differentiate with respect to x, we get y"=-2x-1 Graph using desmos,  1) Graph of -2x-1…

Q: Find an equation of the line tangent to the graph of f(x) = (4x-3)(x+2) at (1,3). The equation of…

A: topic- equation of tangent line to the graph

Q: G lim

A: according to guidelines we should have been able to solve only one question at a time. #5

Q: (c) lim xe-x/2. x 00

A:

Q: |x| lim e* +- + x2 X→0-

A:

Q: lim x→>0¯ -3/x 2 x² e

A: This question is based on limits and L' hospital rule

Q: Graph of ln x

A: Given,         The function is fx=lnx.

Q: lim = e7x- e6x/ex-1 x>0

A:

Q: (e -e-(x-1) lim (х-1) (e*-е) x→1+

A:

Q: 3x e - е -3x e 25. lim -3x + e 3x

A: Finding the limit of the given expression

Q: Lim 4 ht X

A:

Q: x2 lim X→0 e5x

A:

Q: lim (2a +x) X-

A: We find the limit by substitution

Q: Sketch the graph of the function ? = x3-6x2+12. Using the ff. First derivatives (critical…

A:

Q: 1 x-1 x-1 ln x 3) lim

A: Explanation of the answer is as follows

Q: The function g has first derivative given by g'(x) What is 1+x + x3 the x-coordinate of the…

A:

Q: g(x)= cos2x/x2

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

Q: b) lim xã 00-X

A: To evaluate the limit: limx→∞x1x. Solution: We know that, elna=a Using the above property,…

Q: (e) lim V4+ Vx-1 x0*

A:

Transformation of Graphs

The word ‘transformation’ means modification. Transformation of the graph of a function is a process by which we modify or change the original graph and make a new graph.

Exponential Functions

The exponential function is a type of mathematical function which is used in real-world contexts. It helps to find out the exponential decay model or exponential growth model, in mathematical models. In this topic, we will understand descriptive rules, concepts, structures, graphs, interpreter series, work formulas, and examples of functions involving exponents.