Differentiate 1. f(x) = (2x - 1)4 2. f(x) = (x³ + 1)5 5 3. f(x) = (x²-1)² the following using Chain Rule.

Q: 1 1 So (²₁-2²-₂) dx xx+1 x+2.

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Q: Find the critical points and sketch the graph of the function. 1. f(x) = √5 + x

A: We know that Critical points are points where the function is defined and its derivative is zero or…

Q: dr Evaluate - x(x²-4) ² Select one: Ⓒa.- +aresec)+c √√√²4 b. (+aresec)+c (+arcsec)+c O.C. - O d.…

A: This is a problem related to integral calculation. Based on the general formula and concepts we will…

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A: To find the area of region enclosed by given curves.

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Q: X f(x) =< Q 14/15 7 x + 1 3 ;0≤x≤2 ;2≤ x ≤3 5 Tov Then what is the result of 3 (fx) dx 1

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Q: Convert each pair of polar coordinates to rectangular coordinates 1. (3, 225 degrees

A: Since you have asked multiple question, we will solve the first question for you as per our guide…

Q: = Assuming that y = - sec(xy). It will follow that y' Select one: True False y sec(xy) tan(xy) 1-x…

A: Note : As per our guidelines we are supposed to answer only one question if there are multiple…

Q: Find the binomion coefpicient (7)

A: follw the procedure given below.

Q: 1. Evaluate the given integral Q. ² = £ Q L² L² (²x - 3) (x - y) dx dy

A: Let I=∫01∫y2yx-ydxdyI=∫01I2dyHere we…

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A: We have to find out the integral

Q: Evaluate the definite integral. 16 (10y√y +9√y) dy 16 jo (10y√y +9√y) dy = (Simplify your answer.) 4

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Q: a. lim+ 2x 3x²

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Q: answer a and b. Use implicit differentiation to find an equation of the tangent line to the curve at…

A: This question is based on finding tangent line using implicit differentiation.

Q: Assume that x² + y² = 4xy. Then y' Select one: True False 2x-4 4+3y²*

A: Let's solve derivative of function  and maximum value of given function.

Q: y' = X 2 h

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Q: Evaluate the equation f f ² sin (ry)dyda Select one: O a. / O b. 2 c. O d. (²+4) (+4)

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Q: 5. Use the graph to estimate the limits or explain why the limits do not exist. V (a) lim F(x) x-0…

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Q: 4x+8 (x+2) ³ 3). D. Ba -dx

A: This is a problem related to integration. Based on the general formula and concept we will evaluate…

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Q: 3x 4. Find the member of the curve whose slope at any point is and passes through the 4y

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A: This question is related to rate of change, we will solve it using given information.

Q: Find Vf at the given point. f(x,y,z) = x³ +y³ - 2z² + z lnx, (1,4,5) Vf|(1,4,5) = 7i+(-24)j + (75)k…

A: Finding the gradient of f at the given point.

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A: We need to find volume.

Q: 4. Evaluate the following limits. a. lim X→→→+** 2x 3x² b. lim c. lim -3/x X In5 x x²

A: This is a problem related to limit calculation. Based on the general formula and concepts we will…

Q: дz дz Suppose z is a function of r and y and tan(√x + y) = e²². Determine and 3x ду

A: given function tanx+y=ez2

Q: Determine el valor de a € tal que: 80 ex e2x + 1 58⁰ a -dx = R+

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Q: 3. f(x)=x-x³-x²+1 3

A: This is a problem related to derivative of the function. Based on the general formula and concept we…

Q: Determine el valor de a € tal que: 8 et 12x = f -dx = e 2x a +1

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Q: Find the binommal coefficient (4)

A: Topic = Algebra

Q: Suppose the functions f(x) and g(x) satisfy the following: f(2)= g(2) = g(0) = 4 3 2 f'(2) = g'(2) =…

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Q: 1. Graph the function below Using Calculus, find the intervals where the function increases and…

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Q: Find the curvature K and the radius of curvature R at (1,2). (A K= √/2. R=₁ R = √2 (В) K= R= 2√2 2√2…

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Q: Solve the system of differential equations. = - X1 6x1 + 2x2 X2' - 2x1 - 10x2 2, x₂(0) - 22 = x1 (0)…

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Q: 4) Given the points A(1, 2, 3), B(5, 4, 3), and C(2, 1, 2), find angle C

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Q: 1. Evaluate the given integral Q. J[(y - 2x) dA, R where is the region bounded by x = 0, y = x, x =…

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Q: Evaluate the definite integral. 5 4u [(-*--*--* du (u + 3)² 4 5 1 ((---)-D 4u du (u+3)²2 4 (Type an…

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Q: 9. Determine the position of the centroid of a sheet of metal formed by the curve y = 4x - x² which…

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