If f'(a)=, what is the slope of the line tangent to the graph of y = f(x) at the point (a, f(a))? O 72 O 02 -2 2

Q: a) Using all the letters of the word SUCCULENT, determine how many distinguishable arrangements…

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Q: toivencos 3 Evaluate 1 102 22 (nzy) dv G kabriod if G. At the "solid bounded by is the parabolic…

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Q: A tank contains 100 gallons of brine holding 200 lbs of salt in the solution. Water containing 1…

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Q: (13) Value of fr -dx is... xz d 2

A: ∫511 dx/x2  here simple integration is given  ∫511 x-2dx [-1/x]511 -1/11 + 1/5 (-5+11)/55 6/55

Q: -2 xs-1 @ Consider the function f(x)=x² -1<x<1 Ⓡ 2x-1 x21 Ⓒ a. Sketch f(x). b. Evaluate f(x) for x =…

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Q: 2. The diagram below was created using equilateral triangles congruent to ABSR. If OS=a and OT=b…

A: Given equilateral triangles congruents to triangle BSR  and OS = a          OT = b

Q: Evaluate toivancos You G₁ (nty) dv kab

A: To evaluate:  ∫∫∫Gx2+ydvWhere G is the solid bounded by z=y2 and in xy plane x=0 to x=4 and y=-3 to…

Q: g(x) = 2x √1+3x

A: SOLUTION-

Q: Find each function value and the limit for f(x) = (A) f(-10) (B) f(-20) (A) f(-10)= (Round to the…

A: Given problem:-

Q: x=2y-3 and x=1+4y=2y². (-5,-1) x=2y-3 x=1+4y=2y² 2 0 (1,2) 2

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Q: Consider the initial-value problem y' + exy = f(x), y(0) = 1. Express the solution of the IVP for x…

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Q: 8. How many terms are in the expansion of (2x - y)¹⁰? A. 9 B. 10 C. 11 D. 12

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Q: Verify by Differentiation

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

Q: interior to a Ex: let to be any Simple closed Contour C, when flaxed ?? de no dz = 2πT ( Hw a) and…

A: Cauchy integral formula for higher order derivative is :-fn(z0)=n!2πi∫cf(z)(z-z0)n+1dzwhere c is a…

Q: Find the area between f(x)=x²-9 and the x-axis from x = 0 to x = 7. C... The area is square units.…

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Q: xy lim (x,y)→(0,0) x² + y²

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Q: Find the unit tangent vector to the curve defined by r(t) = (4 cos(t), 4 sin(t), 2 sin²(t)) π at t =…

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Q: Given the following equation: y=2x - 3 " y = -3 y = 3 3. Which is the correct graph of the following…

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Q: A body weighing 64 Ib is dropped from a height of 100 ft with an initial velocity of 10 ft/sec.…

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Q: Eliminate the arbitrary constants of the following. Simplify your answers.  4. y = c1x^2 + c2x^3

A: Given problem:- Eliminate the arbitrary constants of the following. Simplify your answers.    4. y =…

Q: Choose the letter of the correct answe. 1) x² (xdy + ydx) = (5- xy) dx a) x ln (5-xy) = 1- cx b) -x…

A: We are allow to solve first question only .If you need rest of answer please upload it separately…

Q: Find the area of the surface generated when the given curve is revolved about the given axis.…

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Q: Find the relative extreme values of p(x) = 20 5 - 3x3

A: Here we have to find the relative extreme values.

Q: cot t(²7) + cos (7) sec (7). DO NOT RATIONALIZE. sin (5) c

A: To solve the following, using exact values.sin5π4 cot2π3+cosπ3 sec7π6

Q: The equation (x-y)dx + ydy = 0 is homogeneous

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Q: 2x+1(4x²_5)³ 3 y = e

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: 3. Let f'(x)=(x-10)(x+2)2(x-1)(x+7). For what values of x is fx) increasing? 0-110 0-9 8 None of…

A: Explanation of the answer is as follows

Q: The boundary of a lamina consists of the semicircles y = √1-x² and y = √25 - x² together with the…

A: Solution

Q: Find the area between f(x)=x²-25 and the x-axis from. x = 0 to x = 6. ... The area is square units.…

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Q: Determine if the following integral converges or diverges: S sin(ln(x))dx

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Q: Problem 3: The graph of h in the figure below has vertical asymptotes at x = -2 and x =3. Find th…

A: Topic = Limits

Q: f(x) = 4e³x9e²x

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Q: Pre-Calculus  :  if x=2x=2 is a solution to the equation x^3-4x^2-31x+70 = 0x3−4x2−31x+70=0, find…

A: We have to find out solutions

Q: Use the ratio test to determine whether the series converges. If the test is inconclusive, then say…

A: We have to check series is convergence or divergence by ratio test

Q: y"+4y=sin 2x, where y(0)=3 and y'(0)=¾

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Q: Find f. f"(0) = sin(0) + cos(8), f(0) = 5, f'(0) = 2

A: Given, f"(θ)=sinθ+cosθ f(0)=5 and f'(0)=2

Q: Find the angle (where 0° ≤0 ≤ 180°) between the following vectors. 0 u 9, 15 >, degrees 0 ||

A: here we have to find angle between two vector  use formula  cosθ = u*v/[u][v] [u] = 92 +(-15)2 [u] =…

Q: Simplify the algebraic expression. 2 2 3 x²y + xy² +y 2 2 x= Y y x 2 x²y + xy² +y³ 2 X 2 y y x

A: Simplifying the given expression

Q: Solve for y + In lyl at x=6: y'=(yx^2 - y)/(y+1); y(3) = -1 4.5

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Q: Problem 1: At what points is the function y = form. 2x²+10x+12 x²-5x continuous? Write your answer…

A: In this question, we want to know the points (in the form of interval) at which the given function…

Q: Question: 3 The volume of a cube is increasing at a rate of 15cm/min. At what rate the side of the…

A: We know that volume of cube is (side)3. That is V=x3, where x is side of a cube. Differentiate V…

Q: 5. 3 C d S a b e porld at t Let λ = 2 be an eigenvalue of an n is correct? (a) |21 - A| ‡0 (b) 21 -…

A: As per guidelines, I can answer maximum one question. Since you have asked for multiple questions…

Q: Initially, there are 250 bacteria and after seven hours, 800 bacteria are observed in the culture.…

A: This is a problem related to differential equation. Based on the growth law we will answer the…

Q: Suppose an object moves along the y axis so that its location is y = f(x)=x² + x at time x (y is in…

A: If position vector of an object is given by  y=f(x) then(i)     Average rate of velocity…

Q: J1 (x²+8)3/20 Find the length of the curve x = y²-n, 1≤ y ≤e². The given curve is rotated 8

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Q: A vector with magnitude 7 points in a direction 295 degrees counterclockwise from the positive x…

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Q: √ √3x + 4 dx

A: According to our guidelines, In case of multiple questions we are supposed to answer the first…

Q: Evaluate the given Laplace transform. L(3t² cos(t)} 6(s³ - 3s) a. (s² + 1)² (s³-3s) b. (s² + 1)³ C.…

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Q: For vectors ?⃗ = ⟨2, −3, −2⟩, ? = ⟨1, −4, 2⟩ Find the projection of vector ?⃗ onto the vector ?.

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Q: (A) ftan (5x)dx dx √9-4x² (C) [sin 6x cos7x dx

A: According to new guidelines if a question contains more than 3 subparts we have to solve only 3…