e following linear plot is derived from a function of the form y = ae", where a and b are constants.
Q: A: Find the lines that are tangent and normal to the curve x + xy - y =1 at the point (2, 3).
A: Since you have asked multiple question, we will solve the first question for you. If youwant any…
Q: Which points on the curve of x^2-xy-y^2=5 have vertical tangent lines? A. (1,-2) B. (2,-1) and…
A: I have used the fact that slope of vertical tangent line is infinity
Q: Please help me with this
A: Explanation of the answer is as follows
Q: Find the equation of the tangent line to the curve y = (2 In(x))/x at the points (1, 0) and (e,…
A: To find the tangent line equations to the curve: y=2 ln(x)x at points (1,0) and e,e2. Note that, the…
Q: If y 3x-5, then find the tangent and normal equations X=3 %3D
A: First we find slope of line. Then equation of tangent is y-y0 = m ( x-x0) For normal…
Q: Find the slope of the tangent line to the curve (a lemniscate) 2(2? + y?)? = 25(2² – y²) at the…
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Q: f (x) = sec(x), x = 4
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Q: Having trouble solving this question.
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Q: The given point is on the curve. Find the lines that are a. tangent and b. normal to the curve at…
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Q: (a) Find the point at y = x³ + x, if the slope is equal to 4. Then find the equation of tangent…
A: I have stated the used method in the brackets
Q: Find all values of the parameter pp for which the line y=2x+1 is tangent to the graph of y=px2+3.…
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Q: use the method in Example 3 to find (a) the slope of the curve at the given point P, and (b) an…
A: Given equation of curve : y = x3
Q: The curve y = ax² + bx + c passes through the point (1,8) and is tangent to the line y= 6x at the…
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Q: The slope-intercept form of a linear equation is: y = kx + q The gradient k equals to tan a. a. show…
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Q: Find an equation of the normal line to the curve at the given point. Express the answer in…
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Q: .3 ax when x= For what values of a and b is the line -3x + y = b tangent to the curve y 4? b
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Q: Find the slope of the tangent line to the curve (a lemniscate) 2(2 + y²)° at the point (- 3, - 1) 2.…
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Q: Find for x? + x +y² + 2 = 3xy the lines that are tangent and normal to the curve at point (3,2).
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Q: Q.3 a).Find equations of the tangent line and normal line to the curve y =x} - x+ 2 at the point (1,…
A: First find slope at given point then use equation of line
Q: Find the equations of tangent and normal lines of the curves at given points: 2?3 + 2?3-9xy=0 at…
A: To find: The equation of tangent and normal lines of the curves at given points. Given: The equation…
Q: S ize Find an equation of the line tangent to the curve defined by x + 5xy + y² = 7 at the point (1,…
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Q: V. Find the equation of the tangent and normal line of the function f(x) = %3! V2x – 1 at the point…
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Q: Find y' and the slope of the tangent line to the graph of (2x - 5y)7 = 3y2 -2 at the point (3,1).…
A: The used formulas are
Q: An equation of the line tangent to a curve at the point (1, 3) is y = x+2. If at any point (x, y) on…
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Q: The equation of the tangent line to the curve x² + y? = 9, at (7,-18) is 7 y = 18 7 (х — 7) — 18 18…
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Q: 53. What is the largest value possible for the slope of the curve y = sin (x/2)?
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Q: a) Find the equation of the tangent line to f at (3, 27/13). y = b) Find the equation of the normal…
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Q: a. For f(x) =-, find an equation for the secant line through the points where x = 1 and x= 5. b. For…
A: Given data - f(x) = 5/x we have to find - a. An equation for the secant line through the point…
Q: Regarding y as the independent variable and a as the dependent variable, find the slope of the…
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Q: Find the equation of the tangent line to the curve y = ( at the point (1, 0) at the point (e, 8/e) y…
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Q: At which labeled point the slope of the tangent line is greatest? > 12.5 11 9.5 6.5 3.5 R 0,6 -5 -4…
A: Slope of the tangent =rate of change According to the graph
Q: Use the graph to estimate the slope of the tangent line to y = xn at the given point. Verify your…
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Q: Find y' and the slope of the tangent line to the graph of (2x-3y)4 = 3y3-8 at the point (2,2). y'=0…
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Q: 3. A function is defined by the equation y = V3x + 4, where does the slope of the tangent line equal…
A: Given, A function is defined by the equation y=3x+4 and the slope of the tangent line…
Q: Find the equation of the line tangent to the curve f(x)=x+ at the point (5, 26/25) 1 %3D
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Q: a. Verify that the given point lies on the curve. b. Determine an equation of the line tangent to…
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Q: Given the curve: xey + 2x - y² = 3.
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Q: (a) Find the point at y = x³ + x, if the slope is equal to 4. Then find the equation of tangent…
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Q: termine the equation of the curve whose tangent line at any point (x, y) i and passes A) y = e* +…
A: We are asked find the equation of the curve.
Q: fx=-3x^2/(5x+2) a) Find the equation of the tangent line to ff at (3,−27/17)(3,−27/17) y=? b)…
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Q: || х? + у? — 4х — 21 3D 0, (5, 4)
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Q: The point P(4, 1) lies on the curve y = Vx - 3. (a) If Q is the point (x, x – 3), use your…
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Q: The point P(6, 1) lies on the curve y = Vx - 5. (a) If Q is the point (x, Vx - 5), use your…
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Q: Diffrentiate y(x) along the curve given by x^y = e^x .
A: given curve is xy=ex Apply logarithm on both sides
Q: For what value of the constant k is the line x+y=k normal to the curve y=x^3
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Q: Find y' and the slope of the tangent line to the graph of (2x - 5y)7 = 3y2-2 at the point (3,1).…
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Q: a. Determine an equation of the tangent line and the normal line at the given point on the curve. b.…
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Q: Find an equation for the tangent line of y = e* that is parallel to the linear equation y = 5x + 17.…
A: Given y=e8x let at point (h,k) on curve y=e8x tangent is parallel to the y=5x+17
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- What is the LOD if the deviation of the blank response is 0.001 and has the equation of the line y=0.285x+0.020?For what value of the constant k is the line x+y=k normal to the curve y=x^3The following figure shows a schematic of the graphs of f (x) and g (x) Knowing that f´ (C) = 0.737, that C = 9.9 and D = 20.4 determine: • The equation of the tangent line to g (x) at x = D (slope mt and intercept e) • The equation of the normal line to f (x) at x = C (slope mn and intercept h) • g´ (D), E, F
- The amount of time a student devotes to class attendance and revision: and the grade obtained are assumed to be linearly related. In a small class of 15 students, the following results were obtained for this linear relationship. Y = 30 +2.50.Y (0.55) (2.96) R'= 0.85 The standard errors are in parenthesis. a,Test the hypothesis that the intereept and slope are individually equal to zero (0) at the S% level of signiticance. (b) Construct n 95% conlidence interval for the true slope. (c)Compute the elasticity of grades with respect to time input and interpret your results. (d) Interpret your R' and explain how it relates to the slope of the regression line. (e) From the results and your answers in (a) to (d), does time input into class attendance and revision really influence the final grade?Fit the best curve (y = a + b x) to the following data, also estimate the stopping distance at 45 mph. Speed X (mph) of car 30 40 50 60 65 Stopping distance Y (ft) 150 195 245 300 340For the curve x - 2t and y = t-1, what is the equation of the normal line when t=2
- 1) For the following function, evaluate and simply: 2) Refer to the following plot of some level curves of ?(?, ?) = ? forThe following table shows retail sales in drug stores in billions of dollars in the U.S. for years since 1995. Year03691215 Retail Sales85.851108.426141.781169.256202.297222.266 Let y be the retails sales in billions of dollars in x years since 1995. A linear model for the data is y=9.44x+84.182 A) Use the above scatter plot to decide whether the line of best fit, fits the data well. The function is a good model for the data.The function is not a good model for the data B) To the nearest billion, estimate the retails sales in the U. S. in 2011. billions of dollars. C) Use the equation to find the year in which retails sales will be $240 billion. .Estimate the standard errors of the intercept and slope se B0 = ? (3 decimal places) se B1 = ? (3 decimal places) Test the hypothesis Ho: B0 = 0 versus H1: B0 not equal to 0 using a = 0.01 to = ? (3 decimal places) Test the hhpothesis Ho: Bo = 2500 versus H1 : B0 > 2500 using a 0.025 to = (3 decimal places)