x3 + 3x2 + 4r +1 dx (r2 + 2x + 2)2

Q: 1. The graph of a function f is shown. Verify that f satisfies the hypotheses of Rolle's Theorem on ...

A: Rolle's Theorem Let f(x) be a function that is continuous on [a, b]  and differentiable on (a, b). I...

Q: Evaluate the integral S 4x4 – 12x² + 7 xdx (2x2 – 3)/4x4 – 12x² + 7 + 2ln|2x² – 3+/4x+ – 12x² +7]} +...

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Q: III. Solve each by factoring then chec- 31. x-x-2 (0 32. x²+ 16x - 36 = 0 33. 8x? - 6x – 5 = 0

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Q: k! Σ 4k k=0 10

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Q: sec3(In x) + sec²(In x) tan(In x) dx Given: 2x Find: du V sec (In x) + sec²(In x) dx tan(ın x) dx ta...

A: On solving this we will get

Q: 1. How many terms are there in an arithmetic sequence with first term 10, common difference of 2, an...

A: Note: As per our company's guidelines we are supposed to answer the first question only. Kindly ask ...

Q: ue Theorem on the given interval? ction satisfies the Mean Value Theorem. continuous on [0, 3] and d...

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Q: Solve the differential equation with appropriate method. Finalize answer free of logarithms and radi...

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Q: One of the following is an improper integral. cln 3 e* dx dx J, xV16 – In x In 2 V4 - ex In 2 CA dx ...

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Q: Find the solution of the following initial value problem: An 14a,-1- 49an- 2; ao = 0, a1 = 6 %3D an ...

A: Let us take an=rn. So, the characteristics equation will be       r2-14r+49=0⇒r=7, 7 Further, we hav...

Q: Show solution/process. 1. f(x) = 2x² – 4x + 5 at the point (–1,11) 2. f(x) = v25 – x² at the point w...

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Q: dy = ky fits this population growth, express the dt A recent report by a country's census predicts t...

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Q: Find the radius of convergence and the interval of convergence. El-1)«(# + 2)2*+1 k2 + 4 A=1 Radius ...

A: Given series ∑k=1∞(-1)k(x+2)2k+1k2+4 want to find radius of convergence and interval of convergence 

Q: f(x) = (x2 + x) (x* - 6x)3 %3D

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Q: 2 cot- (esc") if -3 3. a. Determine if f is continuous or discontinuous at x = 0 and at x = 3. If di...

A: For the solution of the problem follow the next steps.

Q: 6) A function y =e-2x is defined numerically for some data range x. It can be entered using: (а) у -...

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Q: 1+ In x 6. Find f(x) so that when u = f(x) the integral J tan(f(x)) dx can be rewritten as | cot u (...

A: Solve by integration

Q: s(x) = X-4 Find the x-values (if any) at which the function is not continuous. Which of x2-2x-8 the ...

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Q: 4 tanz dr 2. The value of the definite integral (b) (e) 1- (d) 0 (a) 1

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Q: Find h'(2), given that f(2) = -5, g(2) = 4, f'(2) = -2, and g'(2) = 3. %3D f(z) Express your answer ...

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Q: u du Form Answer 5sinx dx Ex. J a+ 2cOsx 3+ 2cosx -2sinxdx uż du -5V3 + 2cosx + C 3 15. Given: •dx 5...

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Q: dz 4z+z' ,2

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Q: y(x^2+y^2-1)dx+x(x^2+y^2+1)dy=0 solve using integrable combinations

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Q: 3. The graph of a function g is shown. 1. (a) Verify that g satisfies the hypotheses of the Mean Val...

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Q: ind the values of c that make f continuous everywhere: { Sa² – c² if x 3

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Q: 1. It is the value for natural exponential fur 2.It is a function which is continuous at eve 3. It i...

A: We will solve 3 parts only 

Q: f = f (x, y) = u? + 3v, y = uv

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Q: MAT

A: Graphical representation:

Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. x) C...

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Q: 15 x 15

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Q: 1+ In x tan(f(x)) Find f(x) so that when u = f(x) the integral | dx can be rewritten as cot u du . А...

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Q: As x approaches 0, the left and right limits equal 3. However, the actual y-value at that point is -...

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Q: зах X-Vx

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Q: Given F(s) = L(f), f(t), a, b, L, n are constants. Show the solution. 12 228 1) s4 $6 2) L²s²+n²n²

A: find inverse laplace transform ?

Q: Use the binomial serles to find the Maciaurin serles for the function. 1 f(x) - (1 + x) Σ (x) = %3D

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Q: Use the definition of Taylor series to find the Taylor series (centered at c) for the function. f(x)...

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Q: Evaluate the integral V4x4 – 12x2 +7 xdx

A: Using integration of square root of x2 - a2 and follow step 2nd . 

Q: t f be a function that is concave up everywhere. Suppose we would like to use the tangent line at x=...

A: If f is concave up so f''>0 and follow step 2nd . 

Q: 20. Given: S 10 -dx Find: formula

A: Here we have to integrate the given function.

Q: 7. Using integration by parts evaluate the integral /(z- 2x)e-3 dz

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Q: Use the binomial series to find the Maclaurin series for the function. f(x) = V1+ x CO f(x) = 1 + -x...

A: From binomial theorem we know, 1+xn=1+nx+n(n-1)2!x2+n(n-1)(n-2)3!x3+....

Q: Use sigma notation to write the Taylor series about x = xo for the functi e*; xo = 6 k=0 e6 k! k=0 k...

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Q: Problem #2 Use Cramer's Rule to solve the given linear system 2x-y 5 x + 3y =-1

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Q: JUX² +2x-8 dx Evaluate lx + 1Wx + 1)* + 9 = l(x + 1) + Vtx + 1}² – 9|]+c 9ln (+ 1)/(x + 1)² – 9 – 3l...

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Q: rectangular carpet has an area of 220 yd^2 .The width of w is 9 yards less that the length l.find th...

A: Options are wrong I have given you correct answer

Q: 4. If f is a differentiable function of x and y with w = f(x, y), x = r cos 0 and y = r sin 0, show ...

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Q: Suppose you have a dataset with m = 1000 examples and n = 200000 features for each example. You want...

A: Explanation of the answer is as follows

Q: e) Explain how one can use differentiation to analytically determine the slope of a curve

A: If cost revenue given , we differentiate it so we give marginal revenue. 

Q: 1I. Create a table of values for the function and use the result o estimate the limit. You are allow...

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Q: Part of the piecewise-defined function (x – 1) + 2 if 0 < ¤ < 3 f(x) = b if x = 3 mx if 3 < x < 6 is...

A: Given problem:-