Determine whether each of the following functions is (a) continuous (b) differentiable.

Q: Let a(t)=20e^-0.3t ( in milligrams) be the amount of drug in a patients body at time t where t is…

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Q: consider the function y=−3sin(4x−π/2)+1  a) What is the amplitude? b) What is the period?  c)…

A: Disclaimer:  “Since you have posted a question with multiple sub-parts, we will solve the first…

Q: y = sinx, x = 0, y = 1; about y = 1.

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Q: limits

A: L'Hospital's rule apply only when there is 0/0 for ∞/∞ form.

Q: 3. y= x²-3x-4 x+2

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Q: E = 5 -2 -4 3 2 2 -4 -4 -4 0 -3 2 3 2 4 4 -2

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Q: The position of an object at time t is given by the parametric equations x = 3t² + 1t y = 3t² + 3…

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Q: With a curve 56 3 17 x² + y = 6, y = x, y = -2 and x = -2. . Determine its area.

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Q: A poster of area 960 cm² has blank margins of 10 cm wide on the top and bottom and 6 cm wide on the…

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Q: Je(ye-1) dr+e dy, where C' is the semicircle through (0, -10), (10,0), and (0, 10). (Compare Problem…

A: Using green theorem, value is evaluated.

Q: The given integral is equal to cos 3t dt 5 + 3 sin 3t O (1/3) In 15 + 3 sin 3t| + C O (1/9) In 15 +…

A: To find out the integration.

Q: √(√x³ - 2 1/2 + √²) d dax In x++²x+ }\x² +C √√(x³)x=√x + √√2x+C

A: SOLUTION-

Q: Find the area (in square units) bounded by the parabolas x² + 2y - 8 = 0. a. 7.10 sq. units b. 7.01…

A: Here we have to find the area bounded by the parabola.

Q: Find the area of the region enclosed by the given curves. y = 2√√√√x, y = x - 3,x=0, x=4

A: Given y=2x, y=x-3 x=0, x=4To find area of region enclosed between two curves:

Q: I. 7. Evaluate each determinant. -3 4 -5 2 -3 -5 1 5 3

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Q: 1/2 x3 1-x4 1/2 √3 - 2/2 √2/560 16 Option 1 1/11 Option 3 1 15 2 16 dx 1 Option 2 Option 4 15 8 √15…

A: Given, ∫012x31-x4dx

Q: Convert the Cartesian coordinate (-1,-4) to polar coordinates, 0≤ 0 0 Enter exact value. 0-

A: Given, (x,y)=(-1,-4)

Q: If z = 4x - xy², which vector is normal to the plane tangent to the surface of this function at (0,…

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Q: Q1: A- Write the following algebraic expression in its simplest form: 5x+3x²+5x+6 X *+3 25x²-9

A: Please refer to the image below

Q: B. Find the general form of the equation of the tangent line to the given curve at the indicated…

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Q: Use integration by parts to evaluate the integral. 9x Saxe dx dx = S4x ex

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Q: Eliminate the parameter t to find a Cartesian equation in the form * = f(y) for: [x(t) = −2+² ly(t)…

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Q: Question 18 If F is a conservative vector field in R³ and C is a loop (curve whose initial and…

A: To find which thing is true about given line integral.

Q: 11. Given f(x, y) = 6r² - 2r³ + 3y² + 6ry. Determine any local maxima, local minima, and saddle…

A: To find out the local maxima, local minima and saddle points.

Q: Find an equation of the plane tangent to the following surface at the given point. yz e x² + +42=0;…

A: The given equation is;  yzexz+42=0; (0,-7,6).

Q: 2. A cyclist applies a force F with magnitude F = 50N in the same direction as the vector b = 4 j.…

A: We have to find the vectors.

Q: Let F be the vector field defined on the plane by F(x, y) = (x¹+3y, 6x - siny). Let C be the unit…

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Q: Find derivative A) y=sin x/1-cos x B) p(x)= 3/1+10e^4x Simplify answer

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Q: Find the critical point of the function f(x, y) = x² + y² + xy +7.5x C=

A: To find the critical point of the function fx, y=x2+y2+xy+7.5x.

Q: 1. f(x) 2. f(x) = 3. f(x) x² - 4x X 2x x²-9 x² x-2 ; C = 0 -4 ; C = ; C = 2

A: Since you have posted multipart questions i can do first three subparts as per our company…

Q: 1. I. Evaluate each determinant. -5 -3 3 -4

A: Given,            -5-33-4

Q: Find derivative of each; A) m(t)= In(4t^3+tan(5t)) B) h(x)= 4sin^8(5x+1)

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Q: Use a double integral to find the area inside one leaf of r=3sin2*theta

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Q: C) (*) Suppose that the Celsius temperature at the point (x, y, z) on the sphere x² + y² + z² = 1 is…

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Q: Solid S is bounded by the given surfaces. (1) Sketch S and label it with its boundaries. (2) Give…

A: Given problem:-

Q: Find the area of the region bounded by the curves y = y = -x² + 4x. 9/4 11/3 12/15 8/3 none of the…

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Q: S dx -1 x-x² 2³√√x 1423 22 Option 1 Option 3 1425 22 Option 2 Option 4 1521 20 1523 20

A: Given: I=∫-8-1x-x22x3dx   As we know the Power Rule: ∫xndx=xn+1n+1+C ; n≠-1

Q: II. Solve the non-linear equation: 1.) x2 - xy + 2y2 = 16 x-y=2

A: Given:  x2-xy-2y2 = 16        ...(1)x-y =2                         ...(2) To find: The value of x ,…

Q: In 7 + 4√3 2.63391 ≈

A: The given expression is  ln7+43

Q: the Following differential equation ²²=1+ P²

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Q: th each graph with its equation of a. r= cos(20) b. r = cos(40) c. r = sin(40) d. r = cos(50) e. r =…

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Q: Let R be the region in the first quadrant bounded by x^2 +y^2 =4, y^2 = -x+4 and y=0. Set up the…

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Q: Calculate the area of the segment cut from the curve y = x(3-x) by the line y = x. 2 sq. units 1 and…

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Q: The rate of a continuous money flow starts at $600 and increases exponentially at 2% per year for 15…

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Q: The equation P=25sin(2πt)+90P models the blood pressure, P, where tt represents time in seconds.…

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Q: Find the linearization of the function f (x) 1 9x+8 at = -1. L(x) = -9x-10 si Find the true values…

A: This question can be solved using the concept of linearization of function.

Q: 1-1 flood

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Q: VI. Consider the conservative vector field 1. F(x, y, z) = (z cos(rz) -y sin(ry), 2y cos(ry) - ry²…

A: Solved below.

Q: 1-√3-x 4. lim. x→2 4-x²

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Q: Find all the values of x such that the given series would converge. ∑_(n=1)^infinity((−1)^n x^n…

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