Find a formula for the sum of n terms. Use the formula to find the limit as n - 00. n -£ (+ + -) (-/-) /=) lim n

Q: Use part I of the Fundamental Theorem of Calculus to find the derivative of sin(x) (cos(t²) + t)dt…

A: Given that , hx=∫-1sinxcost2+tdt h'x=?

Q: Find all local extreme values of f(x) = - The FIRST local extreme value, moving from left to right…

A: Topic:- application of derivatives

Q: Test Σ n 1 2" n! for convergence

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Q: A particle is moving along the curve having the vector equation R(t) = ti+t²j+ tk. Find the vectors…

A: The given position vector is  Rt=t i + t2 j + t k.   The velocity vector is given by Vt=R't=i+2t j…

Q: For the linear function y = f(x) df dx a. Find at x = 8. ƒ'(8) = b. Find a formula for x = f-1(y).…

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Q: Use the graph of the function f(x) shown below in order to determine all values of a in the interval…

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Q: b) y = (e² + √cos x) c) y = |l−tanx 3x³

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Q: -10 -5 I(X) 10 5 10 5 10 X

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Q: y' + y = y²

A: Given: Now,           y' +y=y2⇒dyy2-y=dtIntegrating both sides we get,⇒y=11-et+c1

Q: Find the indefinite integral. | 15 7 19 – 14 d t8 - dt

A: We have to solve the integral

Q: Determine the area of the shaded region bounded by y=-x² + 6x and y=x² - 2x The area of the region…

A: NOTE: Refresh your page if you can't see any equations. . here we have first, we need to find the…

Q: 5-4-3 2-1 10 9 8 7 6 5 1 y 4 32 3+ 2+ 1 2 234 3 4 5 -6 1 2 3 4 5 X

A: Please see the below picture for detailed solution.

Q: 6) Evaluate dx (x+1)(x² + 4)

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Q: Let y = tan(2x + 2). Find the differential dy when z = 5 and dr = 0.2 Find the differential dy when…

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Q: X 2000 A television camera at ground level is 2000 feet away from the launching pad of a space…

A: A television camera at ground level is 2000 feet away from the launching pad of a space rocket is…

Q: sinx/(4+cosx)

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Q: 1. The position of a particle moving in the ry plane at time t units is given by the vector equation…

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Q: For the equation, find the slope m and y-intercept (0, b) (when they exist). (If an answer does not…

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Q: √= - 4x + 43 x² 11x + 18 dx = +C

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Q: y = -x³ + 9x² - 3 concave upward concave downward Submit Answer x0

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Q: Suppose p′(−1)=−2 and q′(−1)=−5.5.  If r(x)=−7p(x)+10q(x), find r′(−1).

A: We have to find the value of r'(-1).

Q: Find the indefinite integral and check your result by differentiation. (Use C for the constant of…

A: To give the solution with proper explanation for the given problem. To find the indefinite integral…

Q: dy 44. -2,(-1,0) x-2

A: Given problem:- dydx=x-2x

Q: 13. What is the maximum value of the parabola ? 5 0 5 a) y = 3 b) x = 4.9 -Cr- 5 c) y = -1 d) There…

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Q: If √x + √y = 12 and y(1) = 121, find y'(1) by implicit differentiation.

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Q: Consider the function f(x) = 6x¹0+ 3x5 - 2x³ - 3. An antiderivative of f(x) is F(x) A is and n is…

A: The given function fx=6x10+3x5-2x3-3 use the integration formulas, ∫xndx=xn+1n+1+C∫dx=x+C

Q: J dx 4+x²

A: Given,            ∫14+x2dx

Q: If the substitution y = x is made, the integral - 1 64 2 3x³ 3+x² 3x³ 3 + x² .64 18x8 3 + x² S™ [²3…

A: The objective of the question is rewrite the integral  and choose the correct option.

Q: Find the curvature (t) of the curve r(t) = (−4 sin t) i + (−4 sin t)j + (1 cost) k

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Q: Use summation properties and formulas to rewrite and evaluate the sum. 31 Σ [(3i)² – 6i] - i=1

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Q: Evaluate the definite integral. Use a graphing utility to verify your result. 9 [(u - 2) du Submit…

A: Topic:- application of integration

Q: 3. Use the graph off to find the followings. a) b) c) 5 4 3 2 1 f(1) f(-2) 32 --14 -2 -3 234 5.X…

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Q: (g) S 40t² 4t²+25 dt S du = u-atan ¹+C 4² u²+a² (be sure to list the parameters: a,b,u, du...etc)…

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Q: Use a system of linear equations with two variables and two equations to solve. A number is 8 more…

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Q: 1. Evaluate. a) lim x--2 ³-2x² +12 x² +1 x² -8x+7 b) lim x-7 2. What is the average rate of change…

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Q: 8. Use the Chain Rule to find az/as and az/at. z = (y-2x)³, x = s³t², y=s+t²

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Q: Find the function y = y(x) (for x > 0) which satisfies the separable differential equation dy dx 3 +…

A: We have given differential equation  dydx=3+18xxy2 y2dy=3+18xxdx Integrating both sides…

Q: Determine the open intervals on which the graph is concave upward or concave downward. (Enter your…

A: Concept: Concavity: if f''(x)>0 ∀ x∈R implies that f(x) is concave upward  And if f''(x)<0 ∀…

Q: 1 The length of the curve y = x³ + x¹ from x = 3 to x = 4 is: a. b. C. d. 145 16 257 12 99 8 593 48

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Q: - TT V(s) ³3² В where s denotes the length of the edge of the cube. Find ß. = $3

A: Given Vs=β-πβs3

Q: 12. What is the minimum value of the parabola ? 5 0 LO a) x = 3.9 b) y = 3 c) x = 2 d) There is no…

A: We have to find out the minimum value

Q: What is the equation of the tangent line to y=−2x^3−x^2+4x+3 at x=3? Write the tangent line in…

A: We have to find the equation of tangent line.

Q: 5. Which of the following expresses √175 in simplest form ? a) 5√2 b) 5√7 c) 7√5 d) 9√5

A: Given that, the number is 175.

Q: State the domain and range: -15. -10 -5 -10- LO 5 0 -5- 5

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Q: 56. 1 dx V1+9x2

A: Given, ∫dx1+9x2

Q: The graph of g' is given below: W Notice this is the graph of the derivative of g not the graph of g…

A: Given graph of g' is shown below

Q: C. Domain Range D. Domain Range

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Q: consider the plane region R bounded by the graphs of y = 3/4(x + 3)2, y = 3/4(x − 3)2, y = 3 and y =…

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Q: Given the ODE: dy dt - --(t-1) cos(y). 4(0)-3 Estimate y(1) using midpoint method, h=0.5. Present…

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Q: Evaluate the integral using the following values. [x³ dx = 260, x 29 - ·[³x dx = 10, [³dx = 2 (29 -…

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