Let f : R → R, where f(n) = 5 . Answer the following questions. 7x²+3*

Q: Use this definition to find f'(a) at the given number a. f(x) = V5x + 1, a = 3

A: First we find out f'(x) then put x=a=3 in f'(x).

Q: Let f(e) = In[r*(z + 6}*(z° + 6)"] f'(x) =

A: Given: Now,         f'(x)=lnx4x+62x2+69'        =1x4x+62x2+69x4x+62x2+69'…

Q: et f(x) = V42 – x and g(x) = x? hen the domain of ƒ o gis equal to [a, b] for x. | nd || ||

A:

Q: The fuction f(x)=[x] is contionous at a=0 O True O False

A: a function is contionous if right hand limit and left hand limit is equal to functional value at x=0

Q: 6. Use an appropriate substitution to prove f(r)dr = f(a + b – x)dr. %3D

A: We have to prove definite integral property.

Q: . Use the definition of error function, prove that [²' ( ²² ) = √T z

A: On solving this we will get

Q: Let f(r) = 2x + 4. Determine (f oƒo f)(r). %3D (fofof)(x) =

A:

Q: Let f : R" → R with f(x) = /1+ ||x||?. Show thatf€ C.

A: As per the question we are given a multivariate function f from Rn to R , and we have to show that :…

Q: Evaluate the function f(x) = e* + In (x + 7) at c, where –7 < c < 6.

A: Given information : f(x)=ex+ln(x+7) 'c' lies between -7 and 6

Q: For what values of a is Jaʼx – 2a, x2 2 f(x) ( 12, x< 2 continuous at every x?

A: Given : The function is f(x) =a2x - 2a        , x ≥212,                     x&lt;2 .

Q: Describe the range of a) f(z) = 3i – z for Re z > 4

A: Find the range of f(z)=3i-z for Re z&gt;4.

Q: If f(x) = |"(9 – t2)e dt, on what interval is f increasing? (Enter your answer using interval…

A: The function is fx=∫0x9-t2et2dt By second fundamental theorem of Calculus, f'x=9-x2ex2. Set the…

Q: Given f(x,y) = x²y-3xy³. Evaluate 2 S₁² 0 fdx

A: Follow the procedure given below.

Q: 3.Show, by means of the example f(t) = sin t, that f ∗ f is not necessarily nonnegative.

A:

Q: If a F (z) = xy+ i (x² – y²), what is F(-1+ 2i)?

A: The given question  is related to complex numbers.  Given F(z)=xy=xy+i(x2-y2) We need to find…

Q: Let f(x) = V42 – r and g(x) = 2? – a. Then the domain of f ogis equal to [a, b] for T. a and b =

A: fog= (42-(x2-x))0.5       = (42-x2+x)0.5

Q: Find the value of c in the interval (a,b) such that f'(c)=0 for f(x)=(x-3)(x+1)´ on[[-1,3].

A: the value of c is:-

Q: Let z = f(x, y) = 4x² + 2xy + By, Step 1 of 4: Evaluate f(3, 1).

A:

Q: For what values of a is Ja'x – 2a, x 2 2 f(x) : \ 12, x < 2 continuous at every x?

A: Given function is Since f(x) is continuous for every x. So, f(x) is continuous at x=2.

Q: let f(x) = ax+b divided by cx+d.   What conditions on a,b,c, and d guarantee that f^-1 exists?…

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Q: let f(x)= x2 . Find the value c in the interval (0,3) so that fave = f(c).

A:

Q: Let f (x) = 2x3 – 0.0064x? – 1.5x + la (a) Indicate that f(x) = 0 has a root in the interval [-3, 0]…

A:

Q: Consider the function f(æ) = 4x° + 4x7 – 6x? – 6. Enter the antiderivative of f(x) Preview

A:

Q: 2. Let f: [0. ox) →R be the function given by f(r) r2 +2. Is the statement Vrvy((z) > f(y)) (x> y))…

A: We have to solve given problem:

Q: Why is ƒ not a function from R to R if f(x)= ½? b. f(x)= Jx ? c. f(x)=±/(x² +1)? а.

A: Why is f not a function from R to R if,  a) f(x)=1xb) f(x)=xc) f(x)=±x2+1

Q: Given f(x, y) 70x + 60y – 2? – 3y? – xy - - evaluate f(1, 3). f(1, 3) =

A:

Q: Q2.Let The deswative f ù f CaJ= %3D

A: The objective is to find the derivative of the function.

Q: Q2 Let f(x) = c x= 0,1,2,3, . 1-find c ? 2-find EX(X – 1) ?

A: Given a probability mass function; f(x)=c2xx!, x=0, 1, 2, 3, ... 1. We know that a very important…

Q: Use the second fundamental theorem of calculus to evaluate the following: x, x 20 10. [* f(x) dx if…

A:

Q: 2. Let f: [0, o0) R be the function given by f(r) x2 + 2. Is the statement Vrvy((f(x) > f(y)) → (x >…

A:

Q: Deschbe the long run behavior of f(x) 1 As x 0o, f(r) → [2 v As x 0o, f(x) ?

A: topic - end behaviour of function

Q: ) Differentiate f(r) = In(v²) + In(10). Hint: Think before differentiate :) you

A:

Q: Di Sfors iade the foihowing on f (x) = 4 3 -) answer Pario evaluade de rrivativeyou re found in Part…

A: The given function is fx=4x3. Obtain the derivative as follows. f'x=-12x-3-1=-12x-4=-12x4

Q: Let F (x) = In tdt then F'(x) = et3 6xe – 3x'e 3xe* – 3x'e

A:

Q: Consider the function f(x) = 8+ (In(z² – 4))* What is its domain and range? (Use interval notation:…

A:

Q: Suppose f(x) = 4nx?e-Tx -e-n for all x € R. Show that f = -f. %3D

A:

Q: 11 what is 3 | f(w)dw? Given that f(x)dx = answer = %3D

A: Here given that ∫39f(x)dx=113 We have to find the value of ∫93f(w)dw

Q: Given that z®h(x) f(x) h(-1) h(-1) 4 7, calculate f'(-1). [HINT: Use the product rule and the power…

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Q: Let f(x)=xeax, where a is a constant.  Q) Show that L{f′(x)}=aL{f(x)}+ 1/s−a.

A:

Q: Use this definition to find f'(a) at the given number a. f(x) = V 3x + 4, a = 4

A:

Q: Let X1,X, f(r;0), where Or-1, 00 0, f(r;0) = elsewhere.

A: Given information: Let X1, X2, …, Xn is a random sample of size n taken from a probability…

Q: Use this definition to find f'(a) at the given number a. f(x) = V6x + 7,

A:

Q: The range of the finction f (x, y) = In(-x²-+1) is 4 O None of these O [0;1] O (*;0] O [0; +**)

A: Note : the range of a real values logarithmic function is the set of all real numbers. i.e. (-…

Q: let f (x) =- , over the interval 0<x<2n , find b 1 a O n 1 b O пп 1 1

A:

Q: Use this definition to find f'(a) at the given number a. f(x) %3D 6х°, а %3D -1

A: Consider the given function. fx=6x5 The objective of the problem is to find the value of f'(a)  at…

Q: Given f(x, y) = - 5a* + 4x?y? – 3y', find | f-(x, y) = fy(x, y) = faz (x, y) = fry (x, y) =

A: Please refer the attached image for complete solution.

Q: Use FTC I to prove that if |f '(x)| ≤ K for x ∈ [a, b], then |f (x) − f (a)| ≤ K|x − a| for x ∈ [a,…

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Q: Determine the following a) f(r² -x=1)dx

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Q: for f (z) = z – Z where does f (z) exist?

A:

Q: Find the value of c in the interval (a, b) such that f'(c) = 0 for f(x) = (x – 3)(x + 1)? on [-1,3].

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.