Find and b such that the following function is continuous at x=( [x] – 2a x < 0 f(x) = 3 x = 0 cos(2x 5) + 6 x > 0 -

Q: g. -3+i

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Q: 5. If fvr² - 25 5. If [ Vx? - 25 dx is transformed by trigonometric substitution, then it will be…

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Q: 4. S 9-x- dx

A: Given problem:-

Q: c) Find the general solution to the differential equation = 3x(y + 8).

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Q: 14. Write the solution set for the general solution. Write the solution set on the interval [0, 2n).…

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Q: Find the derivative of function f given by S(1) = =! X-1 3 x+3'

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Q: V4.01 V4.01 Give your answer correct to Use differential to estimate the value four decimal places.…

A: topic- differentials

Q: Ql: If f(s,t) = s²t+ In(t² – s) find the value of a) atas Q2: For the following function prove that…

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Q: Determina the vector field of F. F(1, y) = yi -j

A: Please see the below picture for solution.

Q: Solve for the differential equation: dy/dx - ytan x = cos x

A: To find the solution of the linear differential equation of first order y'+Py=Q, where P and Q are…

Q: 2. If y = find the differential dy. Hence, estimate the value of 1 + (1.023 1 +

A: topic- differentials

Q: x" Find radius and Σ Va3" 9. convergence and interval for this series n=1 n

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Q: Use the chain rule to find the derivative of: cos(7 + 8x)

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Q: 22. Suppose the velocity of a particle moving on the number line is given by v(t) = 61² – 4t for…

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Q: 21. 3* 3=*-x+'(12x² – 4) dx

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Q: ind the average value of the function over the glven Interval and all values of x In the Interval…

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Q: Determine all the relative minimum and maximum values, and saddle points of the function h defined…

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Q: Find F as a function of x and evaluate it at x = 2, x = 4 and x = 9. :- F(x) = (t + 8t – 4) at F(x)…

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Q: If f(x) = 4,/¤In(x), find f'(æ). %3D Find f'(2). Submit Question

A: Given

Q: y=x nd y=x+2 Revolve the area about the x-axis. Using circular ring method, the volume of the solid…

A: The given curves are; y=x2 and y=x+2. And the bounded region is as shown below; Apply the circular…

Q: P2: (e* sin x + x ln x) dx

A: The given integral is:∫exsinx+x lnxdxWe need to solve the above integral.

Q: Find the 5th order Taylor polynomial about a = r for sin x.

A: To find Taylor polynomial for given function

Q: Q5: Find equations for (a) the tangent plane and (b) normal line at the point P, on the given…

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Q: find the area of the shaded region

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Q: 1 is convergent or 1) Use the Integral Test to determine whether the series divergent. ' (3n– 1)?…

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Q: Find the curvature and the radius of curvature at the stated point. r(t) = 9 cos(t)i + 7 sin(t)j +…

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Q: One set of cylindrical coordinates of the point with the rectangular coordinates (2, 2, 4) is:…

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Q: 2. Write the given (total) area as an integral. a. The area above the x – axis and below y = 4 – x2…

A: Let's find.

Q: 9. Find the local and absolute extreme values on k(x)=(x-2)° +3 on | the interval [0,5].

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Q: Find and classify all the critical points of f (x,y) = 7x – 8y + 2xy – x² + y³.

A: For critical points put partial derivate=0

Q: -1 Su(u² + 3)! du

A: We need to solve integral.

Q: Find the length of the curve z(t) = e“ cos(t), y(t) = e“ sin(t) for 0<t<7. %3D Give an exact answer,…

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Q: P1:

A: Solving

Q: dy into 11. The rationalizing substitution y = u° transforms J 7(1+ В. 6 f и du D. 6J TFu² du С. 6 /…

A: Given problem:-

Q: 6- Give ā = [A, B]and b = [F,E], find VProj(b onto ā) and SProjd onto b). Resolve d into…

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Q: d d Calculate ri(t) · r2(t)] and ri(t) x r2(t)] first by differentiating dt dt the product directly…

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Q: Solve the following system of differentia dx = 4x – z dt dy Зу dt dz = x + 2z dt

A: To solve the given equation.

Q: P5: |V4- 9x?dx 4 –

A: Let's find.

Q: Condense the expression to the logarithm of a single quantity. (log3(x - + 1) + 2 log3(x – 1)] + 6…

A: Let's find.

Q: Determine whether F(x, y) = 2x²yi+ 8xy j is a conservative vector field. If so, find a potential…

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Q: Use the graph of the parabola to fill in the table. (a) Does the parabola open upward or downward? O…

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Q: Match each graph type with its corresponding function.

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Q: Given line M=-ax+ by+ c, b+ 0 What is the y intercept of the function? C-M -M-C OM-c

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Q: Use Green's Theorem to evaluate the integral. Assume that the curve C is oriented counterclockwise.…

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Q: 10. Find the area bounded by 2. Hhe curves y=8x-x²0ind y=3x

A: topic - area bounded by curves

Q: Let F(x) = You also know that a = 10, f(a) = 2, f'(a) = 15, f'(aª) = 11 f(x*) and G(x) = (f(x))“ .…

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Q: If 0 = Ø and R= 4/2, then F2 = %3D 4V2 F, F, V8 08 O 2 04

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Q: Find a formula for the general term a, of the sequence, assuming that the pattern of the first few…

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Q: After substitution is performed, which of the following is equivalent to (4r249)7 dx? 45 8 du u? 13…

A: We have to use the u subsitution method

Q: Evaluate the line integral. The simple curve is C is y = x² starting at (0, 0) and ending at (1, 1).…

A: We can solve as follows