-1 if x <0 (x) 3D{0 if x 0

Q: to this answer. Evaluate the left-hand limit of as f (x) = x8. 16-2x O 1/2 O -1/2 O undefined

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Q: Given the triangle 30 find the length of side x using the Law of Sines. Round your /36° 17° final…

A: Given,            The triangle is shown below :

Q: Egay wants to fence a rectangular grazing area along a straight river (no fence is needed along the…

A: Given problem:- Egay wants to fence a rectangular grazing area along a straight river (no fence is…

Q: irvature and the radius of curvature at the stated poi r(t) = 6 cos(t)i +6 sin(t)j+ 7tk; t= 2 r the…

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Q: Step 1 In pert (a), it was found that the two planes were 200 miles apart and getting closer at the…

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Q: Find the two x-intercepts of the function f and show that f'(x) = 0 at some point between the two…

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Q: A man 6 ft tall is walking at the rate of 3 ft/sec toward a streetlight 20 ft high. At what rate (in…

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Q: Use the appropriate Product Rule to evaluate the derivative, where ri(t) = (9t, -10, -t°),r2(t) =…

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Q: Evaluate f s 2°ds О а. 2"(sin2 - 1) (In2)2 O b. 2(sln2 - 1) (In2)2 O C. 2* In2 O d. 25 In2

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Q: The triangle ABC is defined by the vertices A(1, -2, 2), B(1, 4, 0) and C(-4, 1, 1). Let M be the…

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Q: Q2) Convert the polar function r tan20 to cartesian.

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Q: Is Rolle's theorem valid for the function f(x) = Vi-x on the segment [-1,1]? a. No since the…

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Q: (1 f(x) ={ 5 if x = 4 at x = 4 if x + 4 x - 4

A: limit continuity differentiability at x=4

Q: Solve the D.E dy – (2x/1- y2)dx = 0

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Q: Find the total distance traveled by a body and the body's displacement for a body whose velocity is…

A: Note:- Since you have asked multiple question As per our policy, we will solve the first question…

Q: 1. Water is being poured at the rate of 2 n m³/min. into an inverted conical tank that is 12-meter…

A: The water is leaking at the rate of π/2 m³/min.

Q: A ladder 9 meters in length is leaning against a vertical wall on level ground. As the bottom end of…

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Q: Find the absolute extrema of the function on the closed interval. f(x) = cos 7EX, = COS 0, minimum…

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Q: 2-y QI) Evaluate the integral f dx dy using polar coordinate

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Q: QI) Evaluate the integral dy dx using polar coordinate

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Q: 0.125 А. f(8t) dt | 0. 0.25 B. f(1 – 4t) dt = 2.5 c. f(5 – 2t) dt =

A: Given that,

Q: . 2 28x -15x dx 4x + 7. +C %3D

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Q: dx = x(1 – y) dt dy у(х — 1) dt

A: Solution of the problem as follows

Q: None c) cosh x + C sinh x +C 2 sinh x +C cosh x +C

A: The given integral,      12∫ex-e-xdx

Q: DO NOT include spaces in between characters. * Using implicit differentiation, find the slope of the…

A: We can solve this as follows:

Q: At what rate is the distance between the planes changing? Step 1 Let s denote the distance in miles…

A: Topic:- geometry and application of derivatives

Q: a. f(x) = 4x + 11 find: f'(-2) b. f(x) = 2x2-5x 3 find: f'(2)

A: Given: f(x)=4x+11 f(x)=2x2-5x-3

Q: A line with positive slope passing through (-1, 1) and intersects the parabola y = x² at the point P…

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Q: Which of the following yields the value 318? 3 (8х + 7у) dxdy 0 °0 (8x + 7y) dydx 0 °0 none of the…

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Q: Helene invests Php 5,000 in an investment that earns 6% per annum. How many complete years doe it…

A: Topic = Algebra

Q: Find the limit. NOTE: Enter the answer using round brackets. t2 + 1 1 lim ttoo\ 6t2 +7' 5t (?, ?)

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Q: Q2) Solve the D.E dy – (2x/1- y²)dx = %3D

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Q: Q3) Find the Area bounded by the curves y? = and x = 2y – y².

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Q: Descibe the level curves of the surface f(x.y)=x-4y. O a Hyperbolas Ob.Parabolas Oc Crdes Od Elipes

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Q: Evaluate: | (cosh²2r+ sinh²2r) dr (A 2r +C 1 -sinh 2r +C 2 B -sinh 4r +C 4 D r +C E None

A: cosh²(2r)+sinh²(2r)= cosh(4r) ∫cosh(x)dx= sinh(x)+C, C is a constant.

Q: 12t – cos 31) dt sin7t sin4t dt = A True B False

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Q: 1 Let f(x)= J. dt. Find the derivative f(x). -dt. t4 +5 e2x none of the choices

A: Use the concept of derivative of an antiderivative and simplify.

Q: Consider the series 0 n=1 2+n3 For what values of p does it converge? I. p> 1/2 II. p< 2 O l only O…

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Q: 1. The graph of a function y = a/b(x-h)+k shown below. -1 -40 Algebralcally determine two different…

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Q: 22 – 9x? = 1 4.

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Q: 4. Find an equation of the tangent plane to the surface x = u? + 1,y = v³ + 1,z = u + v at the point…

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Q: Describe the largest set S on which it is correct to say that f is continuous хx* + ху — 5 а. f(х,…

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Q: Evaluate the following integral using Trigonometric Substitutions Method: 1- x dx y =

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Q: 4. Find the area of the region that lies under the graph of f over the given interval. a. f(x) = 2 -…

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Q: (a) Show that the integral test applies, and use the integral test to determine whether the series…

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Q: Evaluate: / sech[in cosr Janx dx A -2 tan-1(e cosx) +c cOsx B) None 2 tan -(e cOx) + C COSA D - 2…

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Q: Q3) Evaluate triple integral f Lx - y²)dz dy dx.

A: The given problem is solved below in detail.

Q: -2e dx

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Q: Evaluate the following integral using Partial Fractions Method: x³ + x? y = dx х2 + х — 2 -

A: Follow the procedure given below.

Q: Use the First Fundamental Theorem of Calculus to answer the ff. If F(x) = tvt +1 dt, evaluate F(1),…

A: Given: Now,          F(1)=∫11tt+1dt=0. Here,               F'(x)=xx+1⇒F'(1)=2 Further,…