11. For what values of "a" and b is the function is continuous at.x31 f(x) = ( 3ax +b: x>1 %3D 11: x= 1 5ax-2b; x <1

Q: A continuous tunction y=f(x) is known to be negative atx=2 and positive at x=6. Why does the…

A: A continuous function y=f(x) Given :f(x) is negative at x=2  and f(x) is positive at x=6 We know…

Q: Suppose that g is a continuous function. Find the general solution of y" – y = g(t).

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Q: Suppose f is continuous everywhere, and | f(x) dx = -1 and 3 Find f(2)dz. f(x) dx 2. Find dx. Cannot…

A: As per our guidelines we are supposed to solve only one question i.e. the first question. For the…

Q: - { S 1² – 3 if r -1 2. Determine the constant k such that the function f(r) is continuous at r =…

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Q: Find the length of the curve e^x / 2 + e^-x /2 between x=0 and x=1

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Q: 4. Find the extrema of the function f(x) = Vx (x + 1) and the intervals on which its graph is…

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Q: Q2) The critical points of the function F(x,y) = x + 3xy + y3 O (0,5) O (1,0) none of others O (1,1)…

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Q: Suppose we have a revenue function given by R(z) = 6z- az?, %3D = 10? where a is a constant. What…

A: Given Rx=6x3-αx2 To find the value of α when average value is $20 for x=10

Q: Find a point c satisfying thr MVT for the given function and interval  y=x/x+2 [1,4]

A: Given query is to find the value of c.

Q: of of and Find for the following function. f(x.y) = e xy In (2y) of dy

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Q: 18: Which of the following functions has no critical points? A: f(x) = -x² + x² B: C: f(x) = x³ + x2…

A: This is the question of multi-variable calculus.

Q: 17. Suppose the radius r, height h, and volume V of a cylinder are functions of time t, and further…

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Q: 9. 6) Suppose that g is continuous and that g(x) dx = 2 and g(x) dx = 16. Find g(x) dx.

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Q: Ql.a- for what value of (k) is the function y= f(x) continuous at x=2 V7x + 2- V6x +4 -2 sx and x #…

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Q: If f(x) is an even, continuous function for which = 4 and dx = 4, then f (x) dx 3 2

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Q: 54. Is the function given by SEx + 4, for x s 3, 2x – 1, for x > 3, g(x) continuous at x = 3? Why or…

A: The given function is;  g(x)=13x+4for x≤32x-1, x&gt;3 we have to check the given function is…

Q: Зx2 — 1 Q7- Let f(x){ cx + d Vx + 8 if x 1 Determine e and d so that f is continuous everywhere (as…

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Q: 2 If f is continuous and f(x) dx = 14, find | xf(x?) dx.

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Q: We have found the following Wronskians. W = -e-³x; W₁ =-e-2x(4+ex)-¹; W₂ = e¯x(4+ e*)-¹ We want to…

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Q: 7. For what value of the constants A and B is the function f continuous on (-0o, 0)E AV-x+6-1 for x…

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Q: 1. Suppose that f(x) = -ar/2 + bæ/2. Reparameterize this function in terms of the location of the…

A: given fx=-ax32+bx12 differentiate the function with respect to x f'x=-32ax32-1+12bx12-1…

Q: If we use Simpson's rule for a function f(x) = X +1 with n=4 , then the approximate of S f(x)dx is

A:

Q: 8. If f is continuous and f(x) dx = 12, find f(2x) dx. 0.

A: Given f is continuous and ∫08f(x)dx=12

Q: Sx+2, if x 1 Value of k that will make f(x) continuous on (-0, 00) is ....

A: K=3 makes f(x) continuous.

Q: If f:R→R is a continuous even function, then | F(x)dx is necessarily equal to -5 O10 O Cannot be…

A: A function is even if f(-x)=f(x)

Q: Suppose that g and h are continuous functions and that S8(x) dx = 5, h(x)dx =-1, and h(x) dx = 3.…

A: There is no such rule of division of two integral.

Q: if x3. then h(x)is continuous at if x = 3 (b) (0,4) x-3 - Let h(x) =32x + 1 (a) 3 (c) (-0, 3) (d)…

A: As we know that a function is said to be continuous at a point x=a when…

Q: 55. Is the function given by S + 4, for x s 3, 2x - 5, for x > 3, F(x) continuous at x = 3? Why or…

A: Function is given by F(x)=13x+4 for x≤32x-5 for x&gt;3 now show that it is continuous at x=3 or not.…

Q: '12 9. If f is continuous and f(x) dx = 20, find f(2x) dx.

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Q: 4ex +x-k if x 0 be continuous everywhere?

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Q: (a) The cost of producing 5-gallon water bottles is given by C(q) = 0.005q? + 2q + 1000. If 2000…

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Q: 2 + 7x if x < 4 Let f(x) if x 2 4. For what value of the constant c is the function f continuous on…

A: Given function is: fx=cx2+7x       if x&lt;4x3-cx          if x≥4 We know that a function is…

Q: 3. Suppose that {f(t)} = F(s) with F a differentiable function and that L{f'(t)} Exists. Then…

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Q: Consider the function f(x, y) = e-xy It is possible to state that f reaches global extremes (global…

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Q: Previous Question 8. Compute the following estimate of 10-1 f(x) dx using 8- the graph in the…

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Q: 1. Where are the following functions continuous? x F(x) = ex + 4-x3 G(x) = 3x5 - 4x? H(x) = x-5x3…

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Q: 4) Find the value of the constant k so that the function (1 – k, if z<3, f(z) = 1– kr, if 123, is…

A: This question is related to limit and continuity of a function, we will use condition for a function…

Q: For what value of the constant a is the function continuous on (-0, 0). for r 1 f(x) ax a =

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Q: 16 8. If f is continuous and f(x) dx = 18, find f(2x) dx. %3D

A: Given integral, ∫016f(x) dx =18

Q: A continuous function y f(x) is known to be negative at x = 2 and positive at x=7. Why does the…

A: Given that f(x) is a continuous function.

Q: if x1 O No, since g(x) is undefined at x=1. O Yes, and g'(1)=3. O Yes, and g'(1)=8. O No, since g(x)…

A: Given

Q: 9) A function y(x) is increasing and has upward concavity on the interval [-2, 3]. Would a…

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Q: 9 3 Iff is continuous and f(x) dx 8, find f(x2)dx

A: Given as

Q: 4. Consider the conduction of heat in a rod 40 cm in length whose ends are maintained at 0°C for all…

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Q: Show mathematically that MRS is increasing for U=1-ex +e2y and is diminishing for U=lnX +LnY

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Q: 1. Suppose that g(x) > 0 for all r, g(x) has a continuous derivative, g(-2) = 5 8 g(4) = 3 and |…

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Q: Find the value of k that makes function continuous at z=4 |2z + 6 z> 4 5z – k z< 4 f(z) = ualuo…

A: Continuity.

Q: If a company's marginal revenue function is  MR(x) = xe−x/9,  find the revenue function. [Hint:…

A: Consider the given marginal function.

Q: 1. If y = f(x) is a continuous function for all 0 <x< 6, and f(0) = 1 and f(6) = 7, then which of…

A: We use the given graph of the function y=f(x), to answer the given question.

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.