Differentiation of single-variable functions Questions
Math 101 - Calculus and Linear Algebra Past Papers
Practice 21 past-paper questions for Differentiation of single-variable functions in Math 101 - Calculus and Linear Algebra. Get solutions and exam preparation resources.
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1. 8. The derivative of the function y = x* is
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2. 17. The critical points of the function y = x^2 - 3x are
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3. 19. A point on the graph of a function where the concavity changes, is called the
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4. Evaluate dy/dx for the following: (i) y = v(3x^2—4x+5) (ii) x = 2cost, y = 3sint (iii) y = e*sinx
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5. Derive formula to evaluate the definite integral as a limit of a sum. Evaluate the integral $\int_{0}^{1}(2x^2 + 3x + 1)…
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6. The slope of the normal to the curve $x^2 + y^2 = 36$ at $(2,6)$ is given by _______.
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7. Derive tangential and normal components of acceleration of a particle moving along a curve in parametric form r(t). With…
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8. The derivative of a function $z = f(x,y)$ in the direction where it rises most rapidly is
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9. The derivative of $f(x,y) = x^2\sin2y$ at $(1, \frac{\pi}{4})$ in the direction of $\vec{u} = 3\hat{i} — 4\hat{j}$ is .
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10. Find the directions and rates in which the function f(x,y) = x? + y2 + xy increases and decreases most rapidly at the po…
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11. Identify the symmetries and sketch the polar curve $r = 1 + \cos \theta$. Find the area of the region bounded between th…
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12. State second derivative test for local extreme values. Find all local maxima, local minima and saddle points of the func…
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13. Find the directional derivative of a function $f(x,y,z) = x^2 + 2y^2 — 3z^2$ at the point $P_0(1,1,1)$ along the directi…
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14. Find the derivative of $f(x,y) = x^2 + xy$ at $P(1, 2)$ in the direction of $i = 7 + j$.
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15. ## 11. What are the reasons for errors in numerical computation on a computer?
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16. ## 17. What is extrapolation?
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17. Define the derivative of a function at a point. Show that if a function $f(x)$ is differentiable at a point then it is c…
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18. The slope of the tangent to the curve $xy = 1$ at the point $(1, 1)$ is
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19. If the graph of the curve $y = x^2$ is shifted 1 unit upward and 2 units right, then the equation of the new curve is
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20. The function $f(x) = x^2 + \cos x$ is a/an __________ function.
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21. Find the derivatives of the following combinations at the given value of x: i) $(f(x) + g(x))$, x=1
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