Use the graph of f(x) = below to find a number & such that f(z)-0.5 <0.2 whenever 0 < |-2|< 8. Enter the exact answer. >= Number 1 0.7 0.5 0.3 O 2 X

Q: The derivative of f(x)=- Select one: O a. O b. O C. O d. cos x-sin x x² x cos x -sin x X x cos x +…

A: The objective of the question is determine the derivative of the given function and choose the…

Q: 1. Express the following equation in vertex form: y coordinates of the vertex point. 2 = 3x² 12x +…

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Q: Find all relative extrema of the function. Use the Second Derivative Test where applicable. (If an…

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Q: A line passes through points A(-1,-5, 9) and B(8, 5, - 15). A vector equation for the line is 7=(-1,…

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Q: 1. Differentiate the following and for each state whether you have used the product rule and/or the…

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Q: Calculate (t) when k(t) = r(t) = (6t¯¹, 1, 6t)

A: r(t)=6t-1, 1, 6t Formula for  curvature κ(t)=r'(t)×r''(t)r'(t)3

Q: Let -2x² + 6x - 3 for x 0. According to the alternate form of the definition of the derivative, to…

A: We will use properties derivative.

Q: Question 13 (1 point) ✓ Saved Which of the following CANNOT be an acceptable direction vector for…

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Q: J 1 cot³ x O 3 2 dx = In | sec² x − 1| + C --- O 1 tan² x + ln | sec x + C 4 O 1 2 O 1 2 1…

A: I have stated the used formulas in the solution

Q: 2. How much money is needed to establish a fund that pays a research scholarship of $10,000 each…

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

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: Find missing number in the series  3,12,26,45,8,22,41,65,13,32,__,85,18

A: Given data:- The given series is, 3,12,26,45,8,22,41,65,13,32,__,85,18

Q: 10. Which of the following is FALSE about the parabola for the function f(x) = (x + 2)² − 6 a) The…

A: The given parabola function fx=23x+22-6 The general parabola equation y=ax-h2+k where, h,k be the…

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

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Q: [2re™² dr a. 2xe*² + C b. x20x³ 3 @. ex² + C d. x²e² + C + C

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Q: A 13 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 2 ft/s, how…

A: A 13 feet ladder is leaning against the wall. The top slips down the wall at a rate of 2 ft/s. The…

Q: Il balloon is inflated so that its volume is increasing at the rate of 2.9 ft³/min. How rapidly er…

A: Topic:- application of derivatives

Q: The area of the surface formed by revolving the curve x = 2√1-y in the interval 0 ≤ y ≤ 1 about the…

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Q: 4. Given f(x) = 3(x − 2)² + 6, what are the domain and range of f(x)? - a) Domain: {x € R}, Range:…

A: The given function fx=3x-22+6 we have to find its range and domain consider the general parabola…

Q: A manufacturer has determined that the total cost C of operating a factory is C = 2x² + 60x + 200,…

A: Firstly we have to solve for average cost per unit as given in the question.  Then apply…

Q: Find the exact value of cos (-42) √√2 2 (Type your answer in radians.) COS ...

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Q: Find the solution to the differential equation that passes through the origin. z(t) = dz dt = 6te42

A: dzdt=6te4z⇒e-4zdz=6tdtIntegrating both sides we get,⇒zt=-ln-12t2-c14

Q: Find the sum by adding each term together. Use the summation capabilities of a graphing utility to…

A: The given sum is ∑i=164i+5

Q: Procedures and Problem Solving Finding the Domain and Range of a Function In Exercises 7-10, use the…

A: Given: Graph is given

Q: 5. S (2x+1) dx (x+4)*(x-3)6

A: Given:        ∫2x+1dxx+46x-36   =∫2x+1x+4x-36dx substitute u=x+4x-3                 dudx=2x+1…

Q: Solve the following ODE. y' = 2y + x x

A: Here, the given DE is: y'=2y+xx⇒y'=2xy+1⇒y'-2xy=1 Comparing it with y'+Py=Q where P &amp; Q are…

Q: Write the complex number in polar form with argument between 0 and 2. -1-√√3i

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Q: Find the length x to the nearest whole number. 46° 520 21° X

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Q: (3 Ln3 Se ad et +y -4n3 dx 2LnX e .dx 2₂2 √√2 Sxe (4) _x xé dx [Lnce)-Lnce") dx

A: As per our company's guidelines, we can solve only three subparts, please repost other parts as the…

Q: The rectangular coordinates of a point are given. Find polar coordinates of the point. Express 0 in…

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Q: ㅠ -π sec xdx. 3

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Q: A cost function is given by C(x) = 200e-0.5. Calculate the marginal cost when x = 3. Give your…

A: Topic- derivative of a function

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: For a function y = f(x), show that the curvature is given by к(x) = Hint: Parameterize the function…

A: Show that the curvature is given by kx=f''x1+f'x232

Q: Given the Vertices v1 = (3, 1), v2 = (1, 4), v3 (6, 5). Calculate the normal vectors n1 of vertex =…

A: We have to find the normal vector on v1.

Q: Find the indefinite integral and check the result by differentiation. COS X 1 - cos²x dx

A: Recall; sin2x+cos2x=1

Q: Q1: _lim, Q2: lim (x-1)(x-2) x+1 x+01+stnx Q8: lim h-o = (C)-8 x²-16 Q3: f(x)=x²-5x+4 is…

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Q: he limit (if it exists). (If an answer does not exist, enter DNE. Round your answer to four decimal…

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Q: A regression was run to determine if there is a relationship between hours of TV watched per day (x)…

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Q: Need

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

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

Q: Which of the follow is the direction vector of the line 7=(2, 1, 3) + t(-7, 1, 6) (7, 1, 6) O(-7, 1,…

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Q: Find a formula for the sum of n terms. Use the formula to find the limit as n - 00. n -£ (+ + -)…

A: The given sum is limn→∞∑i=1n4+in8n use the Riemann integral formula, limn→∞1n∑i=1nfin=∫01f(x)dx use…

Q: Prove the following, using the definition of a limit (convergence to a point). 3 n+2 lim 2- 004-u =…

A: We have given to prove  limn→∞2-3n+2=2 Taking left hand side of equation LHS = limn→∞2-3n+2 LHS =…

Q: 7-x, x4. Complete parts a through d below. Let f(x) = a. Find lim f(x) and lim f(x). Select the…

A: Given that a limit problem and we solve by  using limit method of right-hand  and lefthand  limit…

Q: 27) Two points A and B are on opposite sides of a building. A surveyor selects a third point C to…

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Q: Use exponential regression to find an exponential function that best fits this data. f(x) = Use…

A: Answer is in next step.

Q: X y y = 1 2 3 4 612 639 654 682 5 732 6 746 Use linear regression to find an linear function that…

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Q: Which of the ff is a valid double integral? -2x [*f* xy dy dx b. f*f* xy dx dy a. C. -2x ** 1²* xy…

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Q: B- The velocity of a particle v (msec-¹) at time t(sec) satisfies the differential dv equation…

A: We have given differential equation  tdvdt=v+t dvdt=vt+tt dvdt-vt=1 Comparing this with differential…