Let f(z) then for all real number the power representation of f is Select one: O True O False

Q: f'(x) =-+e²* +x²and f(1)=. Find f(x) Given

A: Here, given that: f'(x)=1x+e2x+x3⇒f(x)=∫1x+e2x+x3dx+C⇒f(x)=∫1xdx+∫e2xdx+∫x3dx+C⇒f(x)=ln…

Q: 1-r 1 can deduce, by applying the formula at r = -9, that 10" -1/8 1-9 Select one: O True O False

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Q: dx 5x2 + 16

A: Given that a integration and we find the solution of this question by general formula of the…

Q: Let N1 (h) be the approximation of f'(xo) with some numerical differentiation scheme depending on h.…

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Q: Exercise 4. Calculate the convergence set of the following is not enough, a justification is also…

A: Given

Q: y =, x = 1, x = 4, and y = 0 is revolved about the y – axis.

A: Let's find.

Q: The Laplace transform of ,-2r ,3(1-t) dt e is Select one: 1 (s + 3)(s – 2) 1 (s + 3)(s + 2) 1 (s –…

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Q: 3 4 11) –3 0 -5 Ans. r = 2 - 4 5

A: A detailed solution is given below.

Q: QV Determine whether the given differential equations are bomogenous and, if so, solve them. a) xydy…

A: To find out that the given differential equations are homogeneous or not.  According to company…

Q: A factory sells a particular product at a price of (200.01x) in peso per unit. The variable cost per…

A: Concept: Maximum value: To find the maximum value of a function using first and second derivatives,…

Q: dy Find by implicit differentiation dx 4 + 5x = sin(xy*) dy dx II

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Q: Find aly if and of to

A: Differentiation

Q: [9]. Suppose that a ball is dropped from an initial height of 300 feet, and subsequently bounces…

A: The initial fall h=300 The first rise & fall 2*.9× 300 The 2nd rise & fall…

Q: x+6 lim 2. X6 X -36

A:

Q: 3) y"+2y'-8y 0, y(0) = 1, y'(0) = 8.

A: Given:y''+2y'-8y=0y(0)=1 y'(0)=8

Q: dy given the dx Use implicit differentiation to determine equation x° + y? 10. - dy dx

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Q: Find the general form of the equation of the plane containing the point Q(0, –2, 10) and the lin…

A: Given: Q=0,-2,10l1:x=1, y=2t-3,z=5-t

Q: 3. Find the parametric equation of the line passing through the point (-1,0,3) and in the direction…

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Q: As x approaches 5 the value of 2x+ 8 approaches

A: Substitute the value of x in the given equation.

Q: 7. How should the function f(x) = be defined so that it will be continuous at x = -1? (B) f(-1) = 0…

A: We have to find the value of f(-1). Also we have to find the interval in which function is…

Q: dy if y =t! and t=Vx Fin d

A: Let's find.

Q: 6. Calculate the locations of maximums and minimums of the following functions: Show work in…

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Q: Find parametric equations for the line that is tangent to the given curve at the given parameter…

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Q: Use implicit differentiation to find the equation of the tangent line to the curve xy + xy : (8, 1).…

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Q: Classify the statement as either true or false. If f is continuous at x= 2, then f(2) must exist,…

A: Given query is to find statement is true or false.

Q: Find the volume OF the solid obtained by rotating about the y- axis the region bounded by Y= x2 and…

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Q: 2) Use the Chain Rule to express the second derivative of f •g in terms of the first and second…

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Q: To find two real numbers whose sum is 23 and whose product is maximum, we should find the maximum…

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Q: To-42 5-2X-3 (6z) odz dy oe aly de

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Q: Q2. Do as required 3. Evaluate: lim (-) X0 sinx

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Q: Determine the absolute maximum and minimum values of the function f(x) =+x the interval -2sxs2. x…

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Q: .What is the limit of the sequence an = [(n2 - 1)/(n2 + 1)]n

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Q: Always remember the Antiderivatives of Trigonometric Functions. a. J sin x dx =– cos x + C d. S csc²…

A: Note:-  These are multiple sub parts question and according to company guidelinde we can do maximum…

Q: P(x) = 23x – a?. %3D

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Q: To find two real numbers whose sum is 46 and whose product is maximum, we should find the maximum…

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Q: Find the first three nonzero terms of the Maclaurin expansion of the function. (x) = e 6x What is…

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Q: 4. How much should be deposited in an account paying 7.5% interest compounded quarterly in order to…

A: Compound interest

Q: 8x + 1 10. Evaluate the integral / dx. 4.x2 + 12x + 10 11 (a) In |4.x2 + 12x + 10|| tan-(2x + 3) + C…

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Q: 6. lim f(x) = +o, lim f(x) = 0 x-1+ x-1- and f(-1) = -1

A: discontinuity

Q: 12. Evaluate: 212-3V+1 (a) (d) / sec (2) / (b) / sec (20) de dr 1 (e) rVI-1 dr dr 16+9r2 (c) sin t…

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Q: For each natural number n, the expression 2* – 7n - 1 is divisible by

A: Concept: Mathematical induction: Mathematical induction is a mechanism for proving a statement,…

Q: Please

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Q: 8/16/22, 140 PM The Sine & Cosine Laws State whether the given measurements determine zero, one, or…

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Q: Solving berneulli differential equation dy Xp

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Q: ,11,,11 x"yll The expression log can be written in the form 24 A log(x) + Blog(y) + C log(z) where A…

A: logmn=log(m)-log(n) log(m.n) =log(m)+log(n) logmn =n log(m)

Q: To find two real numbers whose difference is 24 and whose product is minimum, we can find the…

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Q: Write a in the form a = a-T+anN at the given value of t without finding T and N. r(t) = (- 2t + 3)i…

A: The Solution is given below

Q: Evaluate the indefinite integral, ſx² sinh x³ dx.

A: To evaluate: I=∫x2sinh x3dx⇒I=∫sinh x3  x2dx

Q: Evaluate the limit x2+ 19x-48 lim x²+9x+112 X- - 16 X a. 13 23 O b. 19 23 O C. 00 O d. None of…

A: The detailed solution is given below Thank you

Q: The volume of the solid of revolution obtained by revolving the region enclosed by the x-axis and…

A: