2. Determine the value of the discriminant for the quadratic equation y = 1.4x² - 6x +5 and use that value and the coefficients of the equation to explain how you know if the vertex of the graph of this equation is above or below the x-axis.

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A: finding the area using upper sum and lower sum.

Q: 2 X Estimate the error if P₂(x) = 1 - is used to estimate the value of cos x at x = 0.2. 2 |Error <…

A: To estimate the error in the given function.

Q: If f(x)=sinx+ 2 cosx-x, find / (1)

A:

Q: Multiply both sides by x²(x + 1) and combine like terms. Ax(x + 1) + B(x + 1) + Cx² 9x - 1 A = = X…

A: The equation is given by:-

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A:

Q: Verify that the hypotheses of Rolle's Theorem are satisfied for f(x) = x² - 8x + 12 on the interval…

A:

Q: Use the intermediate value theorem to determine whether the function f(x) = x + 7x-9 has a root and…

A: X3+7x-9 and x= 1 and x= 2

Q: Compute the line integral f(x² + y)ds, where C is the arc of the circle x² + y² = 16 In the second…

A: To find The line integral, where C is the arc of the circle

Q: The function G (t) = 30 – 8.8 cos (t) models the depth, in feet, of water t hours after 9am. Find…

A: G(t)=30−8.8cos⁡(π4t)Using the power Ruleddxxn=nxn−1ddxcos⁡(ax)=−asin⁡(ax)

Q: Having wrapped up your last project, you begin to pack up when you see a text from Casey. They…

A:

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A:

Q: 10. f(x) = e² 12. h(m): 2 化 Vm

A:

Q: Use the Root Test to determine whether the series convergent or divergent. 5n 2n Σ (-20) ³ n+ 1 n =…

A:

Q: Find the x-coordinate of the point on curve y=In(2x²-11x) where the tangent line is horizontal. Just…

A: The objective of the question is to find the x-coordinate of the point on the curve y=ln(2x^2-11x)…

Q: Find the area A of the sector of a circle of radius 20 centimeters formed by the central angle 1/9…

A: Radius of circle=20 cmCentral angle=19 radian

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A: The graph of derivative  is given below. To find the interval(s) on which the function  is concave…

Q: Find the Taylor polynomials of order 0, 1, 2, and 3 generated by f at a. f(x)=√x, a = 100

A: A Taylor series is given by f(x)=∑k=0∞f(k)(a)k!(x−a)k

Q: If you wish to integrate a function over the top half of the unit ball using spherical coordinates,…

A: To find the limit of integral in spherical coordinates

Q: 0-5-5 x'(t) = -5 0-5 x(t). x( -5 -5 0

A: We have to solve the given initial value problem.

Q: Test the series for convergence or divergence using the Alternating Series Test. 1 1 1 1 1 In(3) +…

A: The given series is .The aim is to find the .Alternative series test:Suppose that  and  then the…

Q: 6. (a) The curve y = x², 0≤ x ≤ 1, is rotated about the y-axis. Find the area of the resulting…

A:

Q: If m is the average (arithmetic mean) of the first 10 positive multiples of 5 and if M is the median…

A: The objective of the question is to find the difference between the median and the mean of the first…

Q: Use the Midpoint Rule with the given value of n to approximate the integral. Round the answer to…

A:

Q: Question 4.21) Evaluate the following limits. sin² (1)-1 1-4 A) lim 2/2+1 B) lim x-0 Question 4.22)…

A: a) limx-infinity x[arc(tanx)-pi/2]According to Bartleby guidelines we solve only one question repost…

Q: (a) Use the figure to find the [ f(x)dx. value of L₁₂ f(x² f(x) dx = -10 f(x) Ax [ 1. 7 in (b) If…

A: We will find

Q: Evaluate the line integral, where C is the given curve. Scx³ y³ ds, ds, C: x = t³, y=t, 0≤t≤3

A: given line integral to evalute

Q: Area = 7 (a) What is [*5(x) 5 f²50 f(x) dx = (b) What is f(x) [ f(x)² is fºfo f (x) dx = [s (c) What…

A: Definite integral :- A deefinite integral has been evaluated between specific limits. This can be…

Q: For this problem, you will need to use the Desmos Riemann Sum Calculator. (This link opens a new…

A: We have to find the exact area bounded by f(x) and the x- axis on the given interval using Left,…

Q: for f(x) Verify that the hypotheses of the Mean-Value Theorem are satisfied √49 – x² on the interval…

A: we have given that

Q: -5 -4 -3 -2 5 4 3 2 -1 -1 1 2 4

A: A graph of the function is given.The aim is to find the values of  for which .

Q: Evaluate the integral: /9 - x² = dx (A) Which trig substitution is correct for this integral? 0x = 9…

A: Given indefinite integral is

Q: Suppose f(0) = 4, f'(0) = 2, f''(0) = 2, and f(3) (0) = 6. Find the third-order Taylor polynomial…

A: The nth degree Taylor Polynomial of a function f(x) centered at the point x=0 is given by

Q: Find the equation of the conic that satisfies the given conditions and graph the equation.…

A:

Q: 3 2 1 0 -1 -2 -3 4 f(x) 8 12 32 [.", 16 20 24 28 32 (a) Estimate (by counting the squares) the total…

A: Method of finding the approximate area:Finding the area of one square.The squares which are…

Q: 1 Evalvate the following integrals (use method of integration by parts): 2 (₁) S (sinth) ² dre

A:

Q: Substitute the expressions from the previous steps. Then substitute (x, y) = (1, 1) and solve for dy…

A: To find the slope of the tangent line to the curve  at the point .

Q: Find the inverse laplace of the following: s+1 3. L¹ { S² + 4s +6 4. [¹ e-38 е a Ans. F(1) =…

A:

Q: Express the limit as a definite integral on the given interval. lim Σ 2x₁² + (x₁") ² Ax, [4, 5] i =…

A: The given limit is

Q: Consider the region bounded by the graphs of x = 0, y = cos(x²), y = sin(x²), and x =

A: Region is bounded by x=0,y=cos⁡(x2),y=sin⁡(x2), and x=π2Rotating the region about y-axis.

Q: Find the value of k that makes the antidifferentation formula true k s 5+4 3 - dx 5 +4 = +C

A:

Q: At a certain instant in time, the number of cars, N, traveling on a portion of a certain highway can…

A: The objective of the question is to find the estimated number of cars, N, traveling on a 1-mile…

Q: A manufacturer of pop-up tents makes 2-person tents and 4-person tents. The profit from the sale of…

A: A manufacturer of pop-up tents makes 2-person tents and 4-person tents. The profit from the sale of…

Q: Determine whether or not F is a conservative vector field. If it is, find a function f such that F =…

A:

Q: Current Attempt in Progress Incorrect. Find the area under P = 120(0.7)' between t = 0 and 1 = 6.…

A:

Q: Let the function y = f(x) be defined by the equation x² + y² + 2x + 4y − 21 = 0. dy (a) Use implicit…

A:

Q: Find the value of k that makes the antidifferentation formula true 1 - dx 3+ 7x k Inl3+ 7xl +C

A: To find the value of  that makes the antidifferentiation formula true.

Q: Transform the given system into a single equation of second-order x₁ = −5x₁ + 7x2 x₂ = -7x1 - 5x2.…

A: We have to transform the given system into a single equation of second order.

Q: 1. Linear Approximations: The TANGENT LINE at a point can also be defined as a linear approximation…

A: The tangent line to a curve at a given point is a straight line that just touches the curve at that…

Q: Find and classify all singular points of the differential equation. (2-x)(1 + x)² y" - 3(1+x) y' +…

A: General form of second order linear equation is :-

Q: Write (x³ - 3x) dx as the limit of a Riemann sum with intervals of equal width and right endpoints…

A: The given integral is