x^2+y=16

Q: I need help with 23

A: To find the slope of the tangent we need dydx dydx=dydtdxdt=ddt(4sint)ddt(3cost)=4cost-3sint=-43tant

Q: 5. Solve for y. Your answer should be EXACT (no decimals). (hint: treat as a quadratic) e2y – 7ey + ...

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Q: suppose u and v are differentiable functions of x. Use the given values o fthe functions and their d...

A: Consider the given information: u2=6u'2=2v2=-3v'2=-4 Consider the given derivative. ddxuvx=2

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Q: Does the graph of Y2 pass through the origin?

A: Do the graph of Y2 passes through the origin?

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A: Consider a and b as the amount of an alloy with 16% gold content and 28% gold content, respectively....

Q: Use implicit differentiation to find dz/ðx and dz/ðy. x² + 4y² + 3z² = 7 dz dy

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Q: I need help with 20

A: We find dydx using implicit differentiation.  x2-xy+y2=32x-y+xdydx+2ydydx=02x-y-xdydx+2ydydx=0xdydx-...

Q: Determine the convergence or divergence of the series

A: ∑n=1∞3nn3 Here, an=3nn3⇒an+1=3n+1n+13

Q: If (5,2) is a critical point for the function y= f(x) and f''(x) is + , what can we conclude regardi...

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Q: Find the inverse of the shown matrix A, if possible. Check that AA-1 = I2 and A-1A = I2.

A: The given matrix is A=034-2 The matrix is invertible if and only if determinant A≠0. determinant of ...

Q: Clairaut'sT heorem If fxy and fyx both exist and are continuous on a disk D, then fxy(a, b) = fyx(a,...

A: Given that: Clairaut's Theorem:  If f x y  and f y x both exist and continuous on a disk D, then f x...

Q: The question is attached

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Q: Where does the periodic function f(x) = 2esin (x/2) take on its extreme values and what are these va...

A: Consider the function:  fx=2esinx2 The given function will be maximum when sin(x/2) =1 because the m...

Q: Find the vertical asymptotes, if any, and the value of x corresponding to holes, if any, of the grap...

A: Given: f(x)=x-4x2-16 We have to find out the vertical asymptotes of f(x) and the value of x correspo...

Q: Investigate the following limit. lim x → 0 sin(1pi/x)

A: Consider the given limit limx→0sin1πx, that is, limx→0sinπx.    

Q: two theorem related questions

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Q: number 7 please

A: Given integral is, ∫4x+10x-2x-12dx

Q: Identify and sketch the surfaces x2 + z2 = y2

A: Given surface is x2+z2=y2. The given equation is in the form of x2a2+z2c2=y2. So, the given surface ...

Q: Chain rule help

A: To find: The value of ddxfxgxxx=2. Calculation:  Use the quotient rule of differentiation uv'=u'v-v'...

Q: Suppose that f(a) = f(b) = g(a) = g(b) = 0 and the second derivatives of f and g are continuous on t...

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Q: Find the first partial derivatives of the function. z = (7x + 8y)7 dz %3D dx %3D dy

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Q: Consider the following. Fx) = * f(x) 4 14 - 32x2 Find the critical numbers. (Enter your answers as a...

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Q: Could you please help me show the work for each question

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Q: Find an equation of the line tangent to the graph of f(x) at the point (5,9): f(x) = e-3x-1o + 8

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Q: 5. Let y=(f(x)+5x^2)^4 and suppose f(−1)=−4 and dy/dx=3 when x=−1. Find f'(−1).

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Q: zoom for a better view

A: We know that simple interest on a given sum is given as: INT=p·r·t , where p is the principal sum, r...

Q: Show that the functions are continuous on their natural domains with examples?

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Q: d y is a differentiable function of x . Write dx dy in terms of x , Y , and dx

A: Dear students as per our rule, in one session we can only solve one question. Please post the other ...

Q: 8x(x^2y^2+x^2+y^2+1) dx =7y(x^2+1)dy

A: Consider the differential equation  8xx2y2+x2+y2+1dx=7yx2+1dy  

Q: Use implicit differentiation to find ∂z/∂x and ∂z/∂y if 3x2+4y2+2z2=5

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Q: The polynomial of degree 3, P(x), has a root of multiplicity 2 at x = 4 and a root of multiplicity 1...

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Q: from the top of a 300-ft light house, the angle of depression to a ship in the ocean is 27degrees. h...

A: Given the angle of depression to a ship in the ocean is 27degrees. Height of the light house=300ft A...

Q: differentiate the function and find the slope of the tangent line at the given value of the independ...

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Q: Suppose that f: R→R is a continuous function, satisfying f(5)=8. What is the value of the limit lim ...

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Q: Calculus Question

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Q: Find the indicated partial derivatives. f(x, y, z) = - i fy(9, 1, 7) + y + z fy(9, 1, 7) =

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Q: If f and g are differentiable, then f g is differentiable.

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Q: The question is attached

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Q: Find the value a>0 such that the tangent line to the graph of f(x) = x^2(e^-7x) at x = a passes t...

A: The given function is fx=x2e-7x. At x=a , fa=a2 e-7a. The derivative of fx=x2e-7x is f'x=2x e-7x-7x2...

Q: Find the first partial derivatives of the function. f(x, y, z) = 3x sin(y – z) fx(x, y, z) = %3D fy(...

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Q: Simplify 4(2y - 6) + 3(5y + 10)

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Q: Let G=5f-g look at graph attached G’(1)=?

A: G(x) = 5f(x) -g(x)G'(x) = 5f'(x) - g'(x)

Q: 2x Let f(x) = 4(5). Which is equal to f(1)? Select the correct answer below: 3 4 27 4 81

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Q: . The profit P from selling x units of a product is given by        P = 560x − 0.2x2. The sales are ...

A: The profit P from selling x units of a product is given by :         P=560x-0.2x2 Now, The sales are...

Q: Find the equation of the tangent line at (2, f(2)) when f(2) = 9 and f'(2) = 3. |3D

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Q: Let R be the region bounded by the following curves. Use the shell method to find the volume of the ...

A: Shell Method: y=f(x) on the interval [a, b] then the volume of the solid about the y axis is V=2π∫ab...