Starting from the definition of derivative prove that if f(x) = 1 then f'(a) = a2

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Q: 1 (1) For the function f(x)=1-. find the following: (x+2)? (ii) f(x+k) (i) f(-x)

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Q: _12. Given: ADEC - A RST, If DE=5 and RS=9, Find the ratio of their areas. 25 b. 5/9 c. 10/18 81/25 ...

A: Given two triangles ∆DEC and ∆RST such that DE=5, RS=9 Also these two triangles are similar to each ...

Q: II. FIND THE RECTANGULAR FORM OF THE FF: 1. 14260° 2. 102305° 3. 42138°

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Q: 4. Prove that given any integer for n, n3 + 2n will be divisible by 3.

A: We have to prove by induction.

Q: Gt) = e2-t ult-2) L{ Gt} = 0 G4) e st dt %3D e2-t st dt Ult-2) 3" e2-t est dt dt 2-t-st e -S-) L{ aw...

A: The function given in Laplace transformation given by; U(t-a) is called the step function and its de...

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Q: A hospital district consists of six hospitals. The district administrators have decided that 48 new ...

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Q: 3—4х dx =? Vx2+6x+1

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Q: a. Consider the system of differential equations given by: Y1(0) Y2(0) -3 34 y, y = -1 where some in...

A: a) consider the differential equation y.=-334-1-αy , y10y20=-71 find the determinant A-λi=0⇒-3-λ34-1...

Q: Consider the graphs below, which give m(x) in the left graph, in black, and n(x) in the right graph,...

A: Given composite function is h(x)=n(m(x)) Differentiate h with respect to x h'(x) = n'(m(x)) × m'(x) ...

Q: 8. Let a be a nilpotent element in a commutative ring R with unity. Show that (a) a = 0 or a is a ze...

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Q: Q3) For the function shown: 1) At what value of x, the function is continuous. 2) Is the function is...

A: For the function f(x) given in graph find out the given questions :- If the left-hand limit and a ri...

Q: 1. Consider the function f(x) = x"e-2x for x > 0, where n is some unknown constant greater than 2. A...

A: Introduction: The point where a function attains its extremum, at that point, there is no change in ...

Q: ACTIVITY If U = {1,2,3,4,5,6,7,8,9,10}, A = {1,2,3,4,5,6}, B = {1,2,3,5,7}, C = {2,4} and D = {8,9}....

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Q: L Write True if the statement is true. If the statement is false, explain briefly why it is so. (a) ...

A: Introduction: An infinite series is classified as convergent when the sum of the series is finite. W...

Q: 3y'''+ 5y'' - y' + 7 y = 0, y(0) = 1, y'(0) = 4, y''(0) = 5.8

A: The main objective is to solve the given differential equation.   In the problem  the roots of auxil...

Q: What is the quotient when x^2 - 25 is divided by x – 5? * Ох-5 Ох-25 O x + 5 O x + 25

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Q: In(n) n=1

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Q: ) Let t > 0 and set tS = {tx : x E S}. Show that sup(tS) = tsup S. %3D %3D

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Q: f(x)=6x-10 , g(x)= x^2+3x+8 (gof)(-2) = %3D 55 none of these 25

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Q: Find the partial differential equation by eliminate the arbitrary constants a,b,c for ax+by+cz=1

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Q: 6. (a) Suppose U, W are subspaces of V. Show that (U + W)° = U°nW°. (b) Suppose V is finite-dimensio...

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Q: On January 1, 2018, Kline Inc. borrowed P9,000 from Harvard Co., and on January 1, 2020, it borrowed...

A: Introduction: When a financial institution gives money as a lender, it charges interest. The amount ...

Q: Q2 Find the limits of the following functions: 2-V-5 1. lim tan2r 2) lim -1 1-t-2 3) lim X0 tan4x 4)...

A: According to our guidelines we can answer only three sub-parts and rest can be reposted. 

Q: 2-6s 5. F(s) = 2s2-5 6. F(s) = 3(s+ 2)-1 + 3(s + 2)-1

A: Introduction: The inverse Laplace transformation is the process to find the function ft such that Lf...

Q: Using the principle of mathematical induction prove that F + F3 + F;+ ... +Fm-1 Fam where F; is the ...

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Q: Market research for a certain ice cream company indicates that if the price per cup of ice cream is ...

A: According to our guidelines we have to answer first three subparts if multiple subparts are posted a...

Q: Q1:- Solve the following DEs:- 2xy = x2 + y² + 1 dy 2ху- dx

A: Let us consider the differential equation Mdx+Ndy=0 The equation is exact if ∂M∂y=∂N∂x If the equati...

Q: a. The value of an investment account has a doubling time of 13 years and $35,000 was originally dep...

A: (a) We can use this formula to compute the deposit after t years, P = P0×2tD, where P0 is the initia...

Q: a) How many edges does a K20 graph have? Answer: b) What is the degree of each vertex of a K20 graph...

A: Since  you have posted a multi subparts question according to guildlines I will solve first  three q...

Q: The degree sequence of a graph is the sequence of the degrees of the vertices of the graph in non-in...

A: We have given that , degree sequence ,  4 , 3 , 3 , 2 , 2. We need to find number of edges. We know ...

Q: A 10 kilogram object suspended from the end of a vertically hanging spring stretches the spring 9.8 ...

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Q: You are an accountant for a manufacturer of radios. The demand function for the tablets is p= 40–4x²...

A: demand function is given as p=40-4x2 where x is the number of tablets produced in millions. cost to ...

Q: 1/t tan t (i) Lt t

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Q: Please solve (a)

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Q: Determine whether the following sequences can be described by a polynomial, and if so, of what degre...

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Q: 4n – 1

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Q: Use the definition of the functional limit to prove the following: (a) lim 4x + 3 = -5. x→-2 (b) lim...

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Q: e-2¤1 + 5x2x% 8. Let y(x1, x2, x3) = #3«3 – 20| and F (x1, #2, T3) = ( n - хо — 2.х1 + sin x3 - (a) ...

A: Solution: Given that

Q: . Read about the Integral Test in Section 11.3 and, specifically, through example 2 to see how 1 the...

A: You have asked two different question. We shall answer first question only. For others kindly post a...

Q: Please give the answer with solution: Question 1. f(0) = 2, n = 0,1,2, ... f (n + 1) = f (n) + f (n)...

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Q: Find the equation of the surface of revolution that is generated by rotating the parabola y = x^2 ar...

A: Equation of surface of revolution of a curve about y-axis is given by x2+z2=r2 where r is the radius...

Q: One of the roots of the polynomial equation 2x^3 + 9x^2 - 33x + 14 = 0 is 2. Find the other roots. *...

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