Use the quadratic formula to solve the equation. Give two forms for each solution: an expression containing a radical and a calculator approximation rounded off to two decimal places. (Enter your answers as comma-separated list.) 5x²2x-6=0 1√31 1.31,-0.91

Q: Find the slope of the tangent line to the given polar curve at the point specified by the value of…

A: r=6cos⁡(θ),θ=π3

Q: 1+x² What is the slope of the tangent to the curve y-- 2x when x = 3?

A: y=1+x22x

Q: Match each of the trigonometric expressions below with the equivalent non-trigonometric function…

A:

Q: y-values 9 8- 7 6 5- * 3 2 1 If f(x) f'(3) = g(x) 1 g(x) h(x) > 2 3 x-values then 4 y-values 4 3 2 1…

A:

Q: A rectangle is inscribed in a semicircle of radius r = 16 as shown in the diagram below. x The area…

A:

Q: Use the nth-term test for divergence to show that the series is divergent, or state that the test is…

A: Consider the series

Q: Find the derivative of the function at Po in the direction of A f(x,y.z)= - 3e cos (yz). Po(0,0,0).…

A:

Q: Find the outward flux of the field F= 8xyi + 8yzj + 8xzk across the surface of the cube cut from the…

A:

Q: Use the gradient to find the directional derivative of the function at P in the direction of PQ.…

A: For a Function f( x , y ), The directional Deivative in the direction of  is given as

Q: Work of 4 Joules is done in stretching a spring from its natural length to 16 cm beyond its natural…

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: Evaluate the indefinite integral S 16 (49 - x2) 19/2 dx

A:

Q: Answer the following questions for the function f(x)=x√x² + 36 defined on the interval -4 ≤ x ≤7.…

A:

Q: The position vector r describes the path of an object moving in space. Position Vector Time r(t) =…

A: Given:The position vector r(t) =

Q: Use Lagrange multipliers to find the minimum value of the function f(x, y) =x² + y² subject to the…

A:

Q: The given curve is rotated about the x-axis. Set up, but do not evaluate, an integral for the area…

A: Recall:Area of the resulting surface rotated about the x-axis :If the curve y= f(x) ,…

Q: Sketch the region enclosed by y = 7x and y = 8x². Decide whether to integrate with respect to x or…

A: In this question, we will find the area of the region.

Q: Use spherical coordinates. Evaluate JJJ y²z² dv, where E lies above the cone 4 = 1/3 and below the…

A: G

Q: Find the differ y = √3 dy= = Evaluate dy fc x = 1, G y =

A:

Q: J 4³ (u + 1)² du

A:

Q: Find f. f(t) f'(t) = t³ + -/-/7₁ t5 t> 0, f(1) = 4

A:

Q: What is the unit tangent vector T(t) on the curve r(t) = (cos(t), 3t, 2 cos (2t)) when t = 0? Select…

A:

Q: Write the expression without absolute value symbols. (Simplify your answer completely.) |n² - 101…

A:

Q: Use the parametric curve, and given value for the parameter, to answer the following question. Use…

A:

Q: 7. Given F(x)=√√√x+3 A. Find (fo (fog)(x) B. Find (9°F) (2) gof) → g (x) X -2 report domain and…

A: f(x)=sqrt(x+3)g(x)=x2-2.

Q: Sketch the region bounded by the graphs of the functions and find the area of the region. f(z)=xe-*,…

A:

Q: xª−12x³+36x² X-6 x4+x³-42x 2) lim ||

A: since you have posted multiple questions in this question which are not interlinked so i have solved…

Q: Use the sum and difference formulas to prove the following identities: 1. sin(x - 1) = sin x 2.…

A: 1.sin⁡(x−π)=−sin⁡x

Q: Find the limit. Use l'Hospital's Rule where appropriate. If there is a more elementary method,…

A:

Q: Verify the identity + 1+cos 0 1-cos 0 2 + 2 cot²0

A:

Q: (a) The graph below is the derivative of f(x), but you are answering questions about the parent…

A: Note: As per our guidelines we are supposed to answer only first 3 subparts.If there are multiple…

Q: Consider the following. x = e-5t, y = e5t (a) Eliminate the parameter to find a Cartesian equation…

A: Consider the following.To eliminate the parameter to find a Cartesian equation of the curve.

Q: (a) Find parametric equations for the line segment that joins the point P(-1,-4, -3) to the point…

A:

Q: Use a graphing calculator or computer to verify the given linear approximation at a = 0. Then…

A: The given function is

Q: Find the exact length of the curve. x = 7 cos(t) = cos(7t), y = 7 sin(t) sin(7t), - 0 ≤t≤n

A: x=7cos⁡(t)−cos⁡(7t),y=7sin⁡(t)−sin⁡(7t),0≤t≤π

Q: The diagram below shows upper and lower sums for the function f(x)=√√x+1 using 4 subintervals. Use…

A: given function

Q: List the four smallest elements of the set. (Enter your answers as a comma-separated list.) {y|y =…

A: {y|y = x2 − 3, x  integers}

Q: (4) y' + (x + 1)y = ex²y3

A:

Q: X

A:

Q: -4-3-2 VA 3 2 1-2 x = – 1 y = 1 3 4 5 x x = 2

A:

Q: Give the partial fraction decomposition for the following function. 2 x²-2x-8 2 2 x-2x-8 ||

A:

Q: Suppose that lim f(x) = 6 x 3 and lim g(x) = 8 x-3 Enter the exact value of lim (fg)(x) 2-3

A: Suppose that .To find the exact value of .

Q: Consider the function graphed to the right. Make sure to use the union symbol, U if needed. The…

A:

Q: The rectangular coordinates of a point are given. Plot the point. (-6√2,-6√2) 5 -10 -5 (r, 0) = y 10…

A:

Q: TO Find the length of the curve y = In (2 sec x) for 0 ≤x≤ xs 6 The arc length of the curve is (Type…

A:

Q: The parametric equations and parameter intervals for the motion of a particle in the xy-plane are…

A: Consider the parametric equation

Q: Given C = x³ – 6x² + 9x +4 13 a) Find C'(x) = Find any critical values of C'(x) b)x= Use interval…

A: Given,

Q: Solve the second order Differential Equations. 4y - 12y + 5y = 0

A: The given differential equation

Q: (b) Suppose that f(x) = 2x^2 − x^4 . Find the intervals on which f is increasing and those on which…

A: Question no. (b):Suppose that To find the intervals on which is increasing and those on which it is…

Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

A:

Q: Find r'(t), r"(t), r'(t) · r"(t), and r'(t) x r"(t). r(t) = 2t²1 - 4tj + (a) r(t) (b) r"(t) (c)…

A: