Suppose x = ₁et + c₂e³t. a. Verify that x = =c₁e¯t + c₂e³t is a solution to x" — 4x' - 5x = 0 by substituting it into the differential equation. (Enter the terms in the order given. Enter c₁ as c1 and c₂ as c2.) + + = 0. help (formulas) b. Find a(t) if x(0) ) = 4 and x '(0) = 1. x(t) = = help (formulas)

Q: Determine if 1781 is divisible by 3, 6, 7, 8, and 9.

A: Determine if 1781 is divisible by 3, 6, 7, 8, and 9

Q: Q3/ Evaluate four of the following integrals. a. S sinx cosx 1+cos2x dx_b. f*¹ dx c x²

A: INTEGRATION

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A: We have to find the formula for A(t).

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A: Topic = Geometry

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A: We have to find the differentiation of the above equation.

Q: Q4) Find the largest eigen value for the matrix A= 54 with x (0)=(7/17 1)

A:

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A: We use the formula as given below:

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A:

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A:

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A: The quadratic and cubic approximation at (0,0) formulas are:…

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A: Here we have given equations of two lines as  : y=x and y=x-2.

Q: A. arcsec(-2) B. arctan - الله ان

A:

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A:

Q: FIND THE FIRST PARTIAL DERIVATIVE fx , fy and fz  OF THE FOLLOWING FUNCTIONS. SIMPLIFY YOUR ANSWERS.…

A: Topic = Derivative

Q: 2 4 cot 4 x dx

A:

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A:

Q: n np ₂ (²+1), J пр I)

A: Topic = Integration

Q: a. x K=I 34 K!

A: We can solve this as follows:

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A:

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A:

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A: The limit definition of derivative of a function at x=a is given by  f'(a)=limx→af(x)-f(a)x-a. For a…

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A: Triangle law

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A:

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A: As we know that; The average rate of change between the interval t1≤t≤t2 is given by: Average rate…

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A:

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A:

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A: The graph of  y =f(x) is concave up on those interval where f"(x)>0 . The graph of  y =f(x) is…

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A:

Q: All continuous functions have antiderivatives. (A) True B) False

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A:

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A:

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A:

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A:

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A:

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A: Solution is done in step 2

Q: Consider the matrices shown below: 1 27 D=-1 01 3 24 Compute tr(DET) 6 E = -1 4 13] 1 2 1 3

A:

Q: Which of the following is not true? C 4dx 4dx A So √X(X+6) = lim So c+∞ ¹0 √x(x+6) 5 dx dx B S = lim…

A:

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A: Given,y=x-6                                                             (1)…

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A: We have to use Newton's Method to make the second approximation.

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A:

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A:

Q: 1 -a 2 y dy 3 (a²-y²)²

A: Given :∫012aya2-y232dy

Q: 9. (20 pts) Find the area between (bounded) by the curves y = x² + 10x and y=2x+9.

A:

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A:

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A: Given :x+3y=75x+2y=-4

Q: 2) Find the average value of the function f(x, y) = 6x + 4y over the plane region R. defined by the…

A:

Q: Q4) Find the maximum eigen value for the system 4 = x ¹ (0) = (1 1) 3] with initial vector

A: This is a problem related to matrix operation. Based on the general formula and concept we will find…

Q: Find the maximum and minimum limits of the function f(x) = - X-2 (x+2)²

A: Given ,f(x)=x-2(x+2)2We know that ,Suppose that x=c is a critical point of fx then, If f 'x&lt;0 to…

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A: We have to find limit of given function

Q: given value of x. Show your complete solution.

A: