Find the values of a and b that make f(x) continuous for all real x.  f(x)= (2^xb+a+1,  x< 0 (ax^2+b(x+3), 0< x <1 (acos (pi x) +7bx, x > 1

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A: Given differential equation is xdy-ydx=2x³dx.  

Q: 17. Let f be the function defined by f(x) = . What is the average value of f on the interval [4, 6] ...

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Q: improper integral conve. •00 dx 79. x² – 4

A: Since we are given with multiple number of question and answer will be according to the guidelines.

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A: y= x2(x-1)at x = 0:y = 0(0-1)y = 0and at x=1, y=12 (1-1)Hence, The graph crosses (0, 0) and (1, 0).

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A: Given :y=x9+5To find : (f(u),g(x)) , dydx and G'(u).  

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A: We will find the critical point for the given function.Also we will find that given function is loca...

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A: As per our guidelines we are supposed to answer only one question at a time. So I am solving the fir...

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Q: Solve the differential equation: 1 + Vx² +r? ) dx 2 xdt

A: Let's find. 

Q: find the linear cost function for an item with marginal cost of $120, and it costs 96,500 to produce...

A: Find the linear cost function for an item with marginal cost of $120, and it costs 96,500 to produce...

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A: Solving the problem by doing the integration.

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A: This question is based on finding equation of tangent line at a point on a given curve.

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A: In this question we have to find the Reimann Integral.

Q: Find lim,-2 f(x) 2 -3 -2 -1 2 3 lim→-2 f(x) = 0 %3D lim, -2 f(x) = 2 lim,-2 f(x) = 1 Does Not exist

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Q: y(2x³ -x²y + y³)dx – x(2x³ + y3 )dy = 0 %3D

A: Follow the procedure given below.

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A: We have to find common Ratio,5th term and nth term for given sequence.

Q: 8. There is a jump discontinuity at x = 2 and f(2) = 3

A: Follow the procedure given below. 

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Q: 1. Create one () piecewise function that has 2 removable discontinuities, 2 infinite discontinuities...

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Q: Solve the differential equation: y dt + t (t + y) dy = 0

A: Given that: y2dt+t(t+y)dy=0

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Q: 3. If f(x)=x² – 2x, find the average rate of change (a) from x = 3 to x= 5 (b) from x = 3 to x= 3+c;...

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Q: 3. Center: (3, -5) radius: 2

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Q: 2. Find equations of the tangent line and the normal line to the curve y = 1+ x2 at the point (1, 3)...

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Q: Consider the following sequence: (a) Write out the first five terms of the sequences.[Give exact ans...

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Q: 6. Find y`and y`for y=sin(x + y). 7. Find y` for sin x+ sin y = 1. 8. Find y` for x cos y = sin(x +y...

A: As per Bartleby guidelines, we are supposed to solve only first question when multiple questions are...

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A: In the figure the blue straight lines are members of some of family which are tangents to the given ...

Q: 10. Let f(x, y) = x²y + y. Find the minimum and maximum values of f subject to the constraint x² + y...

A: Given: fx,y=x2y+y The constraint equation is: gx,y=x2+y2=5   Now apply the Lagrange's multiplier; ∂f...

Q: SOLVE FOR THE FOLLOWING DIFFERENTIAL EQUATIONS. 1.(1+x4)dy + x(1+ 4y2)dx =0

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Q: Jax dix x²

A: To evaluate the given integral.∫ln xx2 dx  

Q: 3. For what values of x does the graph of f (x) = x³ + 3x2 +x + 3 have a horizontal tangent.

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Q: 2 – 100 Evaluate the integral: (A) Which trig substitution is correct for this integral? Oz= 100 sec...

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Q: Evaluate the integral. 32 log 16(x + 32) x+ 32 xp-

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Q: (V64 – 2 Evaluate the integral: 52 (A) Which trig substitution is correct for this integral? - 8 sec...

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Q: Evaluate the following integral. 2 de 1

A: Given that: ∫124-θdθ

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A: Given query is to eveluate the integral.

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A: Follow the procedure given below

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A: Let's find. 

Q: (1) Plot the graph of y = r³ – 3r – 5 = 0, and find where the curve crosses the T-axis and the y-axi...

A: The given function is: y=x3-3x-5=0

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A: