A graphing calculator is recommended. Use a graph to estimate the values of x such that ex > 1,000. (Round your answer to three decimal places.) X >

Q: Change the following integral to polar coordinates and evaluate: 4-x² [2² 0 x² + y² dy dx Sketo

A: To convert Cartesian coordinates into polar coordinates we use the following transformation, x=rcosθ…

Q: 3. Calculate the following limit analytically or show that the limit does not exist. Re- member to…

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Q: Find dy/dx for the following functions:- (2) y = v sinh Vtan x (4) y=2,u = 3x²-2 u²+1

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Q: The solid S has a base described by the circle x² + y² = 1. Cross sections perpendicular to the…

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Q: = Suppose that f and g are functions where f(- 9) = -5 and g(0) be on the graph of y = f(g(x))?…

A: We have, f-9 = -5 g0 = -9 The function is, y = fgx                                .............1 To…

Q: A circle has the equation 4x² + 16x + 4y² = (a) Find the center (h,k) and radius r of the circle.…

A: Given Equation:- 4x2+16x+4y2=0

Q: A V(t) = -1,700t + 32,000; value after 5 years = $23,500

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Q: Find the arclength of the curve r(t) (6 sin t, 2t, 6 cost), -2 < t <2

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Q: Find the standard form of a circle given the following conditions. Sketch the graph. 1. Center at…

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Q: Question = 2 and v(y) Define as the region bounded by the functions u(y) around the y-axis, what is…

A: We need to find volume.

Q: 3. If the derivatives of h with respect to U; for h=²u

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Q: dy dt = e¹+y +}

A: We can answer the question as below.

Q: fcos (x) sin(x) dx

A: We need to find out the integration of the given integrand.

Q: f(t) = 2 2 (3 cos 6t-5 sin 6t)

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Q: Find a vector parametrization of the circle of radius 5 in the xy-plane, centered at the origin,…

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Q: f f(x) = x²√Inx² x . find the derivative of this function f'(x) 1-In x² x²√√In x² A. f'(x) = B.…

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Q: Evaluate the integral (1+lnx)5/ x dx from 1 to e.    Find the indefinite integral: sin(x)…

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Q: 3. f(x,y) tanx - sec²x - cosy

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Q: 1. f(x) = sx (x+1 if x ≤ 0 if x > 0

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Q: Find the directional derivative of the function at the given point in the direction of the vector v.…

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Q: The function f(x) is continuous on the interval [-1,3]. The table below gives some of its values.…

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Q: grow art thrive, eventually reprodur the population. (+/24) 10" ³ = 1×2⁰

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Q: Q15) The Parallel Postulate of Euclid is equivalent to: A) The Plane separation postulate B) Pasch's…

A: Solution

Q: 1 3. f(t)=√3-2t; f(1), f(−3), ƒ(0)

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Q: Find the domain and range of: 1) y = 區 2) y =√1-x², 3) y = x² - 2

A: See this solution in below.

Q: Compare the functions f(x) = x7 and g(x) = 7* by graphing both functions in several viewing…

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Q: Find a vector parametrization for the quarter-ellipse from (5, 0, 6) to (0, −2, 6) centered at (0,…

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Q: (a) Use the information in the table to determine the average rate of change on the intervals i. day…

A: We have to answer there subparts in this question and they are related to rate change.

Q: (2cot 2x² - 2e²) dx A. 1/cot 2x³ + 2e²+ C 2

A: To find out the integration of the given function.

Q: 2. Obtain the general solution. (Let 2C=C) (4x + xy²)dx + (y + x²y)dy = 0 3. Check for homogeneity…

A: Differential equation

Q: C. Find the DE of a family of circles with center at (1, -2). Hint: Equation of circle with center…

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Q: You are planning to donate exactly 5% of your income to charity. Your weekly paycheck is $753.98.…

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Q: Q4: Solve the following integrals:- (1) S x3-2x2 dx (2) √ √² √9-x² (3) [ xả sin xdx (cos-¹4x)…

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Q: 3 1 1 Evaluate Inverse Matrix A¹ = -1 = -1 2 2 1 2 -1 1

A: We can apply  A-1= 1/det.of A *(Adjoints of A)

Q: 2. Use the tables to find the inverse z transforms of the following e. 2z 2z-1 f. 3z 3z +1 9. Z Z T

A: Z-transform

Q: 1. f(x) = x 3x-1

A: Domain of a function is defined as the values of x for which the function is defined.

Q: The base of the solid S is the circle x² + y² = 81 The cross sections perpendicular to the base and…

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Q: Find the area between the x-axis and the curve y = -x² - 2x, -3 ≤x≤ 2.

A: Solution: Given that Curve is y = -x^2 -2x Area between the x axis and the given curve is

Q: Find the composite function f(g(x)). 4. f(u) = 3u²+2u-6, g(x) = x + 2

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Q: 1. fx² sec x³ tan x³ dx

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Q: Find the Differential Equation to the given Solution x sin y - xy² = c

A: To find the differential equation corresponding to given function.

Q: <++ 10 -10-9-8-7-6-5-4-3-2-1 9+ 8- 7 1 6+ 10 4 3 Y 2- L -2- 3 -4- 5 -6+ -7+ -8+ -9+ -10+ 2 3 4 5 6 7…

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Q: X 4 4.9 4.99 5 5.01 5.1 6 f(x) 7 8.8 8.99 7 9.02 9.1 12

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Q: 2. Find the derivatives of Y with respect to x if; x=arc sin ex.

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Q: b. Z Z-3

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Q: 8. (a) Compute the roots of the quadratic polynomial s² + 2s + 5. (b) Is the polynomial s2 + 2s +5…

A: Given quadratic polynomials2+2s+5a.Discriminant,D=b2-4acD=22-4×1×5D=-16D&lt;0so, this quadratic…

Q: Show the complete solutions. Family of circles centered at the line y = 2x. Ans: y" (y-2x) + 2(y')³…

A: Given problem:- Differential equation of family of circles centerd at the line y=2x

Q: Define R as the region bounded by the graphs of f(x) = 6x - 5x² and the x-axis. Which of the…

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Q: Find the values of m and n that make f(x) continuous over (-∞, ∞): f(x) = m= n= 4 x-2 mx² - nx 2x -…

A: Topic- Limits and continuity

Q: y = Clx+ C2e

A: