4 Find the linearization of the function f (x) = x² at x = 1. L(x) = Using this linearlization, ƒ (1.05).is approximately Number

Q: 1 Is the function given by f(x)= 3x+2, for x ≤ 3, 4x-7, for x>3, continuous at x = 3? Why or why…

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Q: Q3/: Find the area r=1- cose and over the region R that lies inside the cardioid outside the circle…

A: See this solution I below

Q: Solve the differential equation (24xy +24y²) + (8x² +24xy)y' = 0 using the integrating factor u(x,…

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Q: B)Convert 20= tan¹r to cartesian.

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Q: State the order of the given ordinary differential equation. ty(6)t5y" + 5y = 0

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Q: * Parallel lines have the slope (m1x m2 )= -1 true O False O

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Q: Find the first derivative of f(y) = y (In³ y) A. 3 (In y + 1) B. 3 (In² y) C. 3y (In² y) + In³ y D.…

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Q: 1. g(x) = Sin 39 COS 32 5 ㅈ

A: The objective is to differentiate the equation.

Q: 2 ln x + ln (x+1)- 1/2ln (x^2+1). Compress the logarithmic expression.  PRE-CALCULUS HW question..…

A: The given expression,   2 lnx+lnx+1-12lnx2+1

Q: -0.51-2-5)dy represents the area of a region bounded by O a. the curve x = 12, the line x = 5, and…

A: We have to choose the correct option

Q: J (tanᎾ - 1)2 dᎾ

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Q: 63 x dx 3√ √x²+1 S √(x² + 1)² + C Option 1 O (x² + 1)² + C Option 3 213 √(x² + 1)² + C Option 2…

A: We have to evaluate ∫x dxx2+13.

Q: For which values of a and b E R is the following piecewise function continuous on R? (sin(2x) + a x…

A: for piece wise function  continuty condition is  limx→0- f(x) =limx→0f(x) = limx→0+ f(x)   now…

Q: Find the area of the surface generated when the given curve is revolved about the y-axis 1 y=(8x)…

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Q: In a certain region there is a uniform current density of 15.0 A/m2 in the positive z-direction.…

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Q: Find the velocity and position vectors of a particle that has the given acceleration and the given…

A: This question is related to vector integration ,we will solve it using given information.

Q: 8 hp zh6 S

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Q: Solve the given differential equation by using an appropriate substitution. The DE is a Bernoulli…

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Q: Find the limit. (If an answer does not exist, enter DNE.) x + 7-8 lim X→ 57 X - 57

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Q: Evaluate the indefinite and definite integral (2e* - 3e-2x) dx

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Q: Using calculus, find the absolute maximum and absolute minimum of the function f (x) = 6x² − 36x + 2…

A: We want to find absolute minimum and maximum .

Q: d²y Find for the following function. 2 dx y= (3x² +1) -5 d²y dx² =

A: On solving this we will get

Q: Suppose fe Cla, b] and f'(x) exists on (a, b). Show that if f'(x) #0 for all x in (a, b), then there…

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Q: At what point do the following lines in R³ intersect? l₁ : (x, y, z) = (1,2,1)+ s(1,0,1), l₂ : (x,…

A: See the answer below

Q: ---(1) (y-2)² + (x - 1)² - 9 ---(2) 3. 16 = x² + y²

A: use for quadratic equation   a x2+bx+c=0x=-b±b2-4ac2a and -1  = i

Q: Find f''(x). f(x) = (x²+6) 6

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Q: Lesson Performance Task At an amusement park, a person spends $30 on admission and food, and then…

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Q: Find the volumes of the solids generated by revolving the regions bounded by the graphs of the…

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Q: Fill in the blank. The symbol C₁ represents a constant. - (6 + C₁e-⁹x)= Write this result as a…

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Q: 1. J tanßsec2ßdß 2. (tan0 – 1)2d0

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Q: The curve y = ax² + bx+c passes through the point (3,6). The line y = 4x + 1 is tangent to the curve…

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Q: 8 11xe-x dx

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Q: 1 A large tank is partially filled with 100 gallons of fluid in which 40 pounds of salt is…

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Q: The volume of a solid E is given by 9-1² 9-x²-y² 1.***** 1 dz dy dx -3 JO 0 (a) Sketch each of the…

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Q: Q4) find the soluation of differention equation using exact equation 1) (1 + x²)dy+(2xydx)=0

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Q: In the year 2000, the population of a small city was 40,000. The population grows at a rate of r(t)…

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Q: Q4) find the soluation of differention equation using exact equation

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Q: Find the solution of the given initial value problem. πT ty' + 2y = sint, y = 3, t > 0 Y ||

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Q: a) Graph the function f(x)=2x-5x + 3. b) Draw a tangent line to the graph at the point whose…

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Q: 3) Use the definition of derivative (do NOT use the short cut method) to find_ƒ'(x) given that f(x)…

A: This question is based on finding slope using definition of derivative.

Q: 5) Find the indicated limit if it exists. √√x+4-2 a) lim x-0 X 8x³+27 b) lim x-1.5 2x + 3

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Q: Q.2)(A) Find a formula for the area of the triangle in the xy-plane with vertices at A(0, 0), B(a₁,…

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Q: 16 f(x) = x² + x>0 " X (a) Find the relative extreme point (s) of f; (b) Find the point (s) of…

A: As per our guidelines we are supposed to solve only three sub parts of the problem. For the first…

Q: 3) The line L: x = 3 + 2t, y = 2t, z = t intersects the plane x + 3y -z = -4 in a point P. Find the…

A: To find the coordinates of P and find the equation for the line .

Q: dx √x²=2x+17 a) sinh xe ta 4 bì ninh XH + C 4 c) minh? X-1 2 d) none of the above

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Q: Jse a graphing utility to graph the function and estimate the limit. Use a table to reinforce your…

A: Using l hospital rule to get limit

Q: x -2x +x= 15; x (0) = 7, x (0) = -16

A: This question is based on diffrential equation solved using Laplace transform.

Q: Prove that: 1- Cos (2) dxdy (¹) where R the region bounded by x+y=1,x=0.y=0

A: Given integral I=∫∫Rcosx-yx+ydxdy Where R is bounded by x+y=1x=0y=0

Q: an to four approximation) y and YOY

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Q: Find an equation for the level surface of the function through a given point. x-y + 2z (1,0, -1)…

A: Concept: Level surfaces: For a function, w=f(x,y,z):U⊆R3→Rw=f(x,y,z):U⊆R3→R the level surface of…