If f(x) = 10x + 17, find f'(-3).

Q: II. Consider the polar curves C₁ : r = 3 (in blue) and C₂ : r = 2-2 sin (in red) and let R be the…

A: Let's solve. Two curves given r=3 and  r=2-2sin(theta).

Q: If a sphere passes through the points A(0, 1, 2) and B(−1, 2, 2) and its center C lies on the…

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Q: Using the method mentioned in Item #7, find the volume of the solid generated by 3 revolving the R…

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Q: 27 3. Explain how you would find the general term of the sequence: 4, -6, 9, - ".

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Q: a. For the function and point below, find f'(a). b. Determine an equation of the line tangent to the…

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Q: [* [b3 - 3 3 dy

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Q: For the cubic polynomial function f(x) = : ax³ + bx² + cx + d, find a, b, c, and d so that 0 is a…

A: Solution :fx=ax3+bx2+cx+d f0=2  givend=2   ... 1critical number :f'x=0f'x=3ax2+2bx+c3ax2+2bx+c=0c=0…

Q: Solve the first order linear ordinary differential equation x sin x dy dx + (sin x + x cos x) y =…

A: Here, the given DE can be written as: xsin xdydx+(sin x+x cos x)y=xex⇒dydx+sin x+x cos xxsin…

Q: 5. Calculate the sum of the first 23 terms of the sequence defined below. tn 10+ 3n, n E N

A: We have to find the sum

Q: a. For the following function, find f'(a). b. Determine an equation of the line tangent to the graph…

A: This question can be solved using the concepts of application of derivatives.

Q: 6. If y = 3√x, then what is y'? A. y' = C. y' = ¹ x 3 x3 B. y' = 1/2 D. y' = ¹/2/2 x3 x 3 7. Which…

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Q: = 0 and y 16k (x-3) = 0. Find the area bounded by the parabolas (x - 3)² - 16ky =

A: Given: (x−3)2−16ky=0 and y2−16k(x−3)=0 Graph of the given curves will be as follows

Q: The gradient of the tangent to the curve y=-3x³ + 4ax² - 5x + 4 at x = 1 is 2. The value of a is 2.…

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Q: Given: vector-valued function R(t) whose derivative R'(t) = (4t, 6t, —12t) (a) If Ř(0) = (-1,4,-5),…

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Q: a) 66, 54, 42, 30, ...

A: The given sequence,      66, 54, 42, 30,.....

Q: 4. Determine the number of terms in the sequence: -45, -32, -19, -6, 410 ***

A: There are 36 terms  in the sequence.

Q: A ball is thrown upward from the top of an 800 foot tower. It's height above ground, h, t seconds…

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Q: Find the area bounded by the parabolas (x - 2)² - 9py = 0 and y² = 9p(x - 2).

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Q: Compute[x² sin(2x)dx. A.- x² cos(2x)+ xsin(2x)+ cos(2x)+C 1 1 B. — — x² cos(2x)+ —…

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Q: Ji 16 sin² x cos² x dx dx B

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Q: Consider the vector-valued function 4t-8 [{m(3. In(3-t), 5,31²-8 8 R(t) 4-1² (0, -1,4), 1. Find the…

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Q: 21. Find lim x-5 A. 2 B. 3 x² - 7x+10 x-5 C. 4 D. 5

A: As per the company guidelines we can solve first question. I hope that the given solution will help…

Q: Find the area of the region in the first quadrant bounded by the curve y = √x² +5, the x-axis and…

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Q: A product can be produced at a total cost of C'(x) = 500 + 100x2 + x³ dollars, where x is the number…

A: Given that; Cost function and revenue function.

Q: What integration technique can be used to integrate: O Integration Formulas O Trigonometric…

A: The given integration is I=∫53+x2dx

Q: 5) ( cos 'x dx -1 Where: u = cos(x) dv = dx

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Q: 2. z = x + 2 У Х x

A: Solution

Q: 7) x¹ 9-x ² dx X 3 2 2 where u-x ² dv = x √ 9-x² dx 2

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Q: z²√(-z² + 1)5 dz

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Q: A company determines that its total cost, in thousands of rands, for producing x  items is (image…

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Q: Solve (x + 1)(x + 2)²(x²-1)dx with and without the even-odd theorems (show both solutions).

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Q: Find the moment with respect to the y-axis of the area bounded by the parabola x = 9y - y² and y =…

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Q: If z is a function of r and y implicitly defined by dz Əz find and dr ду at (x, y, z) = (0, 2, -1).…

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Q: a. Use the definition mtan = lim f(a+h)-f(a) h h→0 b. Determine an equation of the tangent line at…

A: Please refer to the image below

Q: Determine the volume generated by revolving about the y-axis the area bounded by y=x²-1, x=2 and y=C…

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Q: What is the inverse for the function f(x) = 2+3/1-x? A. f1(x)=1-(x-2)³ 1 B. f¯¹(x) = 2+³/1-x C.…

A: Given that:  f(x)= 2+ (1-x)1/3 and we find the value of f-1(x).   Here i attached the solution of…

Q: B. m(x) = D. h(x) = x+2 x²-4 28. What is the removable discontinuity of x²-4 the function f(x) : = ?…

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Q: Which derivative rule is used to derive the Integration by Parts formula? A. The Integration by…

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Q: Find the area bounded by y = x3 +6, y = x and y-6 www. -X.

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Q: Determine the value of x when the slope is its maximum for the function f(x) = 2cos (3x)

A: Given,  f(x)=2 cos(3x)

Q: . Expand the binomial (2x - 1)*.

A: Binomial theorem

Q: Using Pappus Theorem, find the volume formed by revolving about the x-axis the area bounded in the…

A: We have to find the volume.

Q: Find the volume of the solid generated by revolving the region bounded by the given lines and curves…

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Q: Find the derivative of f(x) = ✔ (6x¹ + x² − 1) 5.

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Q: Find the equation of the tangent line to the curve y = 5x² - 7 at a point x = 1.

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Q: 436. The plane that passes through point (4, 7, -1) and has normal vector n= (3, 4, 2)

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Q: 3 S₁² √(√²-√²)³ at dt

A: Using substitution method, integration is solved.

Q: Find the volume of the solid generated by the region bounded by y - x² = -3, x+y = 3 about y = -5.

A: The equation of the curves are given by C1: y-x2=-3 ⇒y = x2-3 C2: x+y=3 ⇒y=3-x To evaluate: The…

Q: 1. Write the polar form of the following complex number Z = 3

A: We know that polar form of complex number z=x+iy is z=r(cosθ+isinθ) Where r=x2+y2θ=tan-1(yx)

Q: ƒ(x)=3x² +6x−9

A: